I’ve had a ZT 0350 in my left front pocket for close to 10 years at this point. Every other knife I’ve tried hasn’t been able to compare for me. It’s been rock solid and can handle the abuse I put it through.
For EDC and my general backup pocket knife for hunting these days, been lovin' the Benchmade Mini-bugout with the Orange grip scales. S30V. Nice and light, and I fall in love with the blade each and every time I use it.
Most mid to higher tier knives move away from assisted opening. With flipper, stud, button lock, or spydie hole, the quality of bearings used just makes it unnecessary. Zero Tolerance offer a great deal of bang for the buck and does have a couple of assisted openers if you want to stay US made. As has been mentioned, Civivi is amazing if you want a Chinese made blade.
ZT 566 if you can find one. It checks your boxes. It is assisted, a flipper, has a deep carry clip and good steel. Have a look at other Zero Tolerance offerings. I usually carry old school Ken Onion Kershaws when I want assisted. They don't have true deep carry clips, but they ride pretty low. The whirlwind, blackout, and avalanche are my favorites. The Avalance has quality steel.
A lot of good choices mentioned but some are not assisted flippers.
OP is there a physical issue that you deal with that limits you to an actual assisted opening knife?