I was denied asylum in Sweden, and I was given four years of entry ban. Now can I apply for a residence permit as a family member of an EU citizen or the asylum rejection will prohibit me from doing so?
A ban should not in and of itself prevent you from applying nor should it lead to an automatic refusal. The standard Swedish authorities have to apply is that three conditions are fulfilled:
- Your sponsor is an EU citizen who has the right to reside in Sweden (i.e. has work or sufficient means not to be a burden to the welfare system)
- Your relationship with this EU citizen is genuine (in case they suspect, e.g., a marriage of convenience, they have to provide some evidence, not the other way around)
- You do not present a current threat to public policy, public security, or public health.
Depending on the reasons for your ban (4 years is long, merely being denied asylum shouldn't necessarily result in a ban, was deception involved?), it might be possible to make a case that you do not fulfill the last condition but it should be an argument based on the threat you currently represent, not an automatic refusal based on the decision in an unrelated procedure. An EU freedom of movement case can overcome everything else, including past immigration violations, earlier refusals, or even a criminal record.
As an extended family member, you also need to prove a dependence relationship with the EU citizen sponsor (they are dependent on you or you are dependent on them). It's not enough to merely claim you are dependent. Here again, the earlier ban shouldn't be an insurmontable barrier but it could invite additional scrutiny and it's easier to cast doubt on such an application than it is on applications by spouses or minor children. The whole process (preparing your application, getting the consulate to entertain it and fighting a negative initial decision which seems like a real possibility) can be quite delicate to navigate, it could be useful to hire a lawyer if you can afford it and know how to find one.