The frame on my external side door to my garage has worked loose from
the wall, resulting in the door not closing properly. I've tried frame
fixings but they don't seem to pull the frame back tightly against the
wall (I think they're specifically designed to not do this). I need
something that will really pull the frame back very tightly against
the wall, and the head of the fixing will need to be level/just below
the surface of the frame.

I've looked around at other fixings but not sure what best to use. The
main problem is that I don't want to remove the whole frame from the
wall, so I can only drill through the frame and into the wall, and the
fixing could pull out as I screw it up tight. I'd thought of hex head
concrete screws but looking at pictures on Toolstation and Screwfix
they don't seem that substantial and with a big enough head to not
pull in to the wood (plus I only need about 8).

Advice much appreciated.