@manukris , I think I have to change my position.
The issue here is whether you are an employee or a trainee. OPT is usually a trainee position and generally falls under the safe harbor ule for FICA. But this is usually with F-1 or similar student visa extension. See Rev. Proc. 2005-11 and administrative Procedural note on the subject. This depends heavily on whether the employer and the "employee" each qualify for the safe harbor exemptions. It does not delve into visa type.
The ) visa type is a non-immigrant work visa ( needs a sponsor just like H-1 visa ).
So my assumption here is that you are NOT on OPT / Trainee status but an employee. Thus your employer has to participate with you on sharing FICA .
Why did you not extend your F-1 visa if you are a trainee ?
Another issue is that for FICA an employer has to participate on a 50-50 basis for FICA contribution. The 2022 year is passed and therefore his books are closed.
Suggest you talk to the employer and seek a solution. It is a case of sleeping dog ....."
When was your visa change affected ? If in October of 2022 or thereabouts it may be better to leave it alone.
Does your employer issue a W-2 or 1042-S ?
Is there more I can do for you ?
