Can using an aftermarket oil filter damage my engine?

General rule of thumb where you can't go wrong is to get an OE-spec, high-quality filter that specified by the part manufacturer to be used in your vehicle. Where you can potentially get into trouble is with purportedly "high-performance" but also very cheap, universal filters.

no, unless it was left loose and all the oil blew out not having lubricating oil it would from not seating the rubber seal against engine block or the oil filter seat