I will guess that either the chrome portion of the cap will pop off allowing you to see the internal screws, or if not, it's possible you will need to disassemble from under the cabinet and pull out through the top.
You should be able to see the thin seam where the smooth chrome cap meets the edge of the brass colored ring. There is an o-ring that helps to seal it and hold it inside, but will probably be a little rotted, making it hard to remove the cap.
It looks like a Kohler style that I've come across a few times.
A little silicone grease on the o-ring and screw threads will make it easier to service in the future.
Ok this is going to drive me nuts. I used to sell this exact faucet, I rmember having a spare handle sitting on my desk for months because we didn;t know where it came from. I used to fiddle with the damned thing whenI was bored. Do you think i can remember what brand the faucet was? Of course not! I want to say moen but it was so long ago I just can't be sure. Anyways, I seem to remember the chrome caps coming off, but you had to get a thin knife edge or something under it to do so.
At the time I sold moen, delta, peerless and taymor faucets, so that should narrow it down some I guess.
Thank you for responding, finally success, had a plumber who was able to turn top off cap, it was a Delta, which looks alot like other's of that era, very much appreciate all those who took time to help, quite the community,
R.W