I'm EU citizen, in 2015 I was deported from UK and got a 10 year ban. The forms i got are IS.165 and ISE.312 yes I have spent time in UK prison and got deported. Question is will I be allowed to enter Ireland by air. My deportation documents don't mention nothing about Ireland.
Given that you are an EU citizen (and not dual citizen of a non-eu country, which could result into different outcomes), there are two potential ways forward. You have the right to enter any EU country except where prohibited (i.e., UK in this case), so just go and hope for the best. Or, you work on undoing the ban and travel freely without any potential problems.
Given your history, I suggest you do not take the first action to enter Ireland.
Why? As part of Common Travel Area (CTA), since 2011 Ireland and the UK share information including, but not limited to, biometric and biographic information which includes legal hisotry. According to Irish government agencies:
The Common Travel Area also involves some co-operation on matters relating to immigration issues. A third country national, for example, may be refused permission to enter Ireland if it is their intention to travel onwards to the UK and they would not qualify for admission to the UK under the Aliens (Amendment) Order 1975. Irish immigration officers have the power to carry out checks on people arriving in the State from the UK and to refuse them entry to the State on the same grounds as apply to people arriving from outside the Common Travel Area. These checks are carried out selectively.
In December 2011, the Irish and UK governments agreed measures to secure the external Common Travel Area border. This includes exchanging biographic and biometric visa data and co-operating on establishing information about failed asylum seekers. There is a joint UK-Ireland Common Travel Area Forum which implements these measures.
While the checks are selective, it might be worth noting that simply presenting your passport will give instant access to your deportation and legal records which, consequently, could lead you into further trouble if the border officers are not satisfied with your explanations, thus leading into entry refusal or worse potential deportation from Ireland as well.
At a more subtle level, to an Irish immigration officer, you cannot convince (if asked) that you will not use Ireland to enter the UK. Why? Simply because there are no checks to enter Northern Ireland (UK) from Republic of Ireland. Such entry is essentially what your ban prohibits.
A discussion at FlyerTalk might be helpful since the case is somewhat similar i.e., travel freedom of EU national with criminal record in the UK.
Disclaimer: I am not an immigration expert, just curious and the information above is collected by a quick web search.