My ps4 keeps on ejecting my discs then beeps constantly

"This is a known issue with PS4's. It happens to a lot of them. the good news is that it is usually fixable. You can first make sure that it's sitting on a flat surface with nothing under it or on top of it. Sometimes removing the rubber feet in the middle of the bottom side of the console will help.

I hope this helps."

There is a screw that's accessible through the HDD slot that controls manual ejection. Try tightening that screw, it's the only related screw you can get to without voiding the warranty.