Looks like pain peeling from a paint job with insufficient prep, cheap paint, or poor application.
Unfortunately, the only real solution is to sand the new paint off and refinish. Since the paint is peeling off, any new paint you apply to that surface will come off with the layer below it, when the original paint continues to peel off.
If only a panel or 2 were repainted, it won't be too bad of a job, but if whole car was painted then you got a ball buster ahead of you.
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