Breezie, a great many variations of .58-caliber Minie-balls were used in the Model 1863 Springfield rifle. Most of those varieties did have 3 grooves. (Technically, they are grooves, not rings - which are raised, but relics diggers have been calling them "rings" for so many years that it's nearly impossible now to get them to change the lingo.)
I assume your question means what bullets the yankees fired out of the '63 Springfields. As you know, the Confederates captured many thousands from the yankees, and of course then fired various versions of CS-made minies from them.
To answer your question, rather than go into all the variations of US-made 3-groove minies, I'll just list the very most common US .58-caliber bullets for the 1863 Springfield. If you went metal-detecting in a 1863/64 yankee camp or fortification, most of the .58s you'd find are (listed in order of "commonality":
1- "generic" 3-groove minie (many variations in groove-depth, shape of "nose," and shape of base-cavity)
2- Williams "Bore Cleaner" bullet, Type 3
3- "Regulation" minie by Williams (has 3 flat-bottomed grooves, a conical cavity, and a roundish nose, was previously but incorrectly called Harpers Ferry minie)
In 1861-63 "Western Theater" sites (which during the civil war meant any states between the East Coast states and the Mississippi River), you'd also find a lot of .577 Enfield minies in yankee sites ...because (contrary to popular belief) the yankees did issue a lot of Enfield ammo to their "Western" troops, for use in either a Springfield or an Enfield rifle.