We have a spigot on the back of the house we are renting, it's actually more like a cap with a round handle (no opening to attach a hose). When I turn and loosen the handle, it opens a valve that allows water to flow to a fountain in the back yard. If I keep turning it, it will come off entirely and water comes directly out.

It's really old and I want to replace it (buy online) but I can't describe it well enough to find this part online. If I could also find a different spigot that would also have a y-valve or something to attach a hose, it would be ideal.

Anyone know of what I am describing? Know it's technical name?

Post a pic.

Probably a gate or globe valve in line to the fountain and you screwed the stem out.

How about replacing it with a hose bib and a hose bib wye. (see images)
Would that work for you? Let me know. Tom