What are the available postdoctoral fellowships in Europe that non-European can apply for? In life Science, What are the available postdoctoral fellowships in Europe that non-European can apply for?
Once joined an EU research center can a non-EU researcher apply for Marie-Curie postdoctoral fellowships?
during a PD interview, PI said, it's not possible once the applicant already joined an EU center?
To answer your second question first, the Marie Curie fellowships require evidence of mobility - specifically, that you haven't worked in the proposed host country for more than 12 months total in the past three years. So if you join a lab in, say, France, after one year you will no longer be able to apply for a MSCA fellowship in France.
However, you'd still be eligible to apply for one hosted in any other EU country where you had not worked for more than 12 months in the past three years.
So, if you're happy and able to move labs, then you would still be eligible to apply for a MSCA fellowship. The full eligibility documents are on the call website if you want to read in more detail.
I don't think there's a short answer to your first question - the EU contains dozens of large scientific funders and probably hundreds of fellowship schemes, with differing requirements. There are likely search tools for specific countries/opportunities which would give a better answer.