I recently noticed that I have different signatures on both of my passports. I acquired my 2nd passport for eligibility to stay at a foreign country to study in a long term. I would like to visit where I was originally from but am afraid if Customs will question my signatures on both of my passports. Will this cause any trouble when travelling? Thank you for your help!
I don't think this is normally an issue. For the most part, you will only be showing one passport. For example, use your European passport in the EU (when leaving or arriving) and use your foreign passport when you enter that country. In third countries, use the passport that shows eligibility to your destination for that part of the journey.
The only time I can think of where you would show both passports is at check-in. At that point the airline may want to show that you are eligible to enter the destination without any visa (if applicable) or necessary paperwork for foreigners (especially with additional Covid requirements). They may also want to see your other passport to see that you are staying legally at the place of departure (otherwise there may be delays when departing).
When departing, the passport control officers (or machines) I've met don't look at eligibility to enter at my destination, they simply check if I am who I say I am and whether they have some problem with me (outstanding warrants, outstanding fines, overstaying one's visa if applicable, etc.). To show that, I only need to show one passport.
Comparing signatures, I think, would only happen if there's some additional suspicion. If that happens, the worst case is that they do some additional verifying to see if the document is genuine. Maybe that includes a check with the country that issued the passport to see if they have a record of you, but I don't think that's a regular scenario.