How to fit a screw into a drilled big hole on wall

Sure. You tap (or drill out and tap) the larger hole for a convenient thread size, and use an M6 threaded insert with that thread size (from personal experience, I suggest not using the helical type unless you have to - if there is no space constraint, a larger-outside-thread solid insert holds up better.)

M6x1 with an outer of M10x1.5 seems to be a common solid insert size that should work with the constraints you've mentioned, in "drill out and tap" mode.

If you have a different mindset or set of tools, you can also weld the existing hole up, redrill and tap for M6 - most folks don't go there first, as getting a good fill on a small hole is tricky - but again, you can drill it out larger first if that is the problem, or drill it out larger and weld in a plug.

What you need to use is a fastener called a "toggle bolt". They come in small sizes (1/8 inch, screw diameter) up to 1/4 inch. Depending on the weight of your item the larger the toggle the more it can support. A toggle bolt is a threaded machine screw that uses a pair of spring loaded wings (anchors) as a nut. Mark the location for the hole and use a slot head screw driver to bore through the dry wall. I'm guessing that the metal you encountered is most likely the lathing for the plaster (or stucco?) wall. Either way,try to make an oversized opening into the bay of the wall. Put the toggle screw through the item and thread toggle wings onto threads. Push the two wings together and wiggle them into the wall opening. The wings will expand behind the drywall. All that's left is to tighten the screwhead. Finito.