Hi,
There is a million and one ways of developing your core with only your bodyweight. Here are a few examples:
Plank, oblique plank, horse stance, lying leg raises, oblique crunches, full boxer sit ups, press ups with rotation, leg circles (great for hip mobility), fire hydrants (great for hip mobility), trail leg (great for hip mobility), 1 on 1 wrestling, superman, glute bridge, oblique touches, wheel barrow races (ensuring strong core position), single leg overhead football squats.
Don’t retrict yourself to just these there are many more!!!