It sounds like you are mainly concerned with stating what your nationality is on the Danish visa application form.

Since you have a US green card and you do not hold a passport, you would likely be traveling with a US re-entry permit (Form I-327), which is a passport-like booklet issued by USCIS that is used in lieu of a passport. You would be submitting the re-entry permit to apply for your Danish visa, instead of a passport, and the visa sticker would be placed in your re-entry permit.

The re-entry permit lists a nationality, which would be the “country of citizenship” that is listed in field 5 of the Form I-131 you use to apply for the re-entry permit. Whatever nationality USCIS prints in your re-entry permit (which, based on other answers, may be Thai, Vietnamese or stateless) is the nationality you should fill out on the Danish visa forms. The Danish authorities are unlikely to question the nationality stated by USCIS or ask for further evidence about that.

(The nationality you provide on Form I-131 should match what you have previously told USCIS when you applied for the green card, or you might be asked to provide further evidence.)

The short, pragmatic answer to your question is: use whatever nationality is printed in your re-entry permit, unless it is clearly wrong.

The “joint Danish travel document” you are referring to is most likely a “fremmedpas” or “alien’s passport”, which is like the US re-entry permit and is issued to Danish residents who are stateless or unable to apply for a passport from their home countries, usually refugees. The Danish alien’s passport will also list a nationality, and ideally that would also match the nationality in your US re-entry permit; if not, you might be asked to explain the discrepancy, which might actually be relatively easy due to the objective confusion about your nationality.

It sounds like you are mainly concerned with stating what your nationality is on the Danish visa application form.

Since you have a US green card and you do not hold a passport, you would likely be traveling with a US re-entry permit (Form I-327), which is a passport-like booklet issued by USCIS that says “Travel Document” on the cover and is used in lieu of a passport. You would be submitting the re-entry permit to apply for your Danish visa, instead of a passport, and the visa sticker would be placed in your re-entry permit.

The re-entry permit lists a nationality, which would be the “country of citizenship” that is listed in field 5 of the Form I-131 you use to apply for the re-entry permit. Whatever nationality USCIS prints in your re-entry permit (which, based on other answers, may be Thai, Vietnamese or stateless) is the nationality you should fill out on the Danish visa forms. The Danish authorities are unlikely to question the nationality stated by USCIS or ask for further evidence.

(The nationality you provide on Form I-131 should match what you have previously told USCIS when you applied for the green card, or you might be asked to provide further evidence.)

The short, pragmatic answer to your question is: use whatever nationality is printed in your re-entry permit, unless it is clearly wrong.

The “joint Danish travel document” you are referring to is most likely a “fremmedpas” or “alien’s passport”, which is like the US re-entry permit and is issued to Danish residents who are stateless or unable to apply for a passport from their home countries, usually refugees. The Danish alien’s passport will also list a nationality, and ideally that would also match the nationality in your US re-entry permit; if not, you might be asked to explain the discrepancy, which might actually be relatively easy due to the objective confusion about your nationality.

It sounds like you are mainly concerned with stating what your nationality is on the Danish visa application form.

Since you have a US green card and you do not hold a passport, you would likely be traveling with a US re-entry permit (Form I-327), which is a passport-like booklet issued by USCIS that is used in lieu of a passport. You would be submitting the re-entry permit to apply for your Danish visa, instead of a passport, and the visa sticker would be placed in your re-entry permit.

The re-entry permit lists a nationality, which would be the “country of citizenship” that is listed in field 5 of the Form I-131 you use to apply for the re-entry permit. Whatever nationality USCIS prints in your re-entry permit (which, based on other answers, may be Thai, Vietnamese or stateless) is the nationality you should fill out on the Danish visa forms. The Danish authorities are unlikely to question the nationality stated by USCIS or ask for further evidence about that.

(The nationality you provide on Form I-131 should match what you have previously told USCIS when you applied for the green card, or you might be asked to provide further evidence.)

The short, pragmatic answer to your question is: use whatever nationality is printed in your re-entry permit.

The “joint Danish travel document” you are referring to is most likely a “fremmedpas” or “alien’s passport”, which is like the US re-entry permit and is issued to Danish residents who are stateless or unable to apply for a passport from their home countries, usually refugees. The Danish alien’s passport will also list a nationality, and ideally that would also match the nationality in your US re-entry permit; if not, you might be asked to explain the discrepancy, which might actually be relatively easy due to the objective confusion about your nationality.

It sounds like you are mainly concerned with stating what your nationality is on the Danish visa application form.

Since you have a US green card and you do not hold a passport, you would likely be traveling with a US re-entry permit (Form I-327), which is a passport-like booklet issued by USCIS that is used in lieu of a passport. You would be submitting the re-entry permit to apply for your Danish visa, instead of a passport, and the visa sticker would be placed in your re-entry permit.

The re-entry permit lists a nationality, which would be the “country of citizenship” that is listed in field 5 of the Form I-131 you use to apply for the re-entry permit. Whatever nationality USCIS prints in your re-entry permit (which, based on other answers, may be Thai, Vietnamese or stateless) is the nationality you should fill out on the Danish visa forms. The Danish authorities are unlikely to question the nationality stated by USCIS or ask for further evidence about that.

(The nationality you provide on Form I-131 should match what you have previously told USCIS when you applied for the green card, or you might be asked to provide further evidence.)

The short, pragmatic answer to your question is: use whatever nationality is printed in your re-entry permit, unless it is clearly wrong.

The “joint Danish travel document” you are referring to is most likely a “fremmedpas” or “alien’s passport”, which is like the US re-entry permit and is issued to Danish residents who are stateless or unable to apply for a passport from their home countries, usually refugees. The Danish alien’s passport will also list a nationality, and ideally that would also match the nationality in your US re-entry permit; if not, you might be asked to explain the discrepancy, which might actually be relatively easy due to the objective confusion about your nationality.