Ys I and II were originally released on some weird Japanese computer in 1987 and 1988 and then got like a hundred ports and remakes. The ones released in the west were Ys I on the Master System in 1988 (there is no Ys II for Master System), Ys Book I & II on Turbo CD in 1990 (probably the most influential version on western gamers but since it was on Turbo CD there were pretty hard limits to how popular it could be; it's available on Virtual Console), and the similar-to-each-other-but-not-identical modern remakes of Ys I & II on PC, PSP, and DS in the 2010s (the PC version is probably best of the modern ones, you can get it on Steam).
Ys III: Wanderers from Ys was originally released on some weird Japanese computer in 1989 and then got console versions that got released in the west on SNES, Genesis, and Turbo CD in 1991. All of them have some issues and the game is kind of divisive in general but the SNES version is probably the worst of the three. Ys: The Oath in Felghana is a remake that made some pretty extreme changes but is in general much better than any version of Wanderers from Ys; it's available on Steam and PSP.
Ys IV: Mask of the Sun on SNES and Ys IV: The Dawn of Ys on Turbo CD (both in 1993) are totally different games made by different developers (neither of which was the original developer of the first three games; they were having some financial problems at the time or something) that share soundtracks and are built from the same basic character/plot/setting/premise outline but their different developers went in different directions from there. Neither came out in the West but both have translation patches now and The Dawn of Ys is much better. The Vita game Ys: Memories of Celceta isn't a remake of either by my understanding but is a new game made by the original developer, who has of course declared that it is the canonical version of Ys IV; it got a western release.
Ys V came out on SNES in 1995. No western release, but there is a translation patch.
And then the series went dead for like 8 years until Ys VI (aside from continued rehashes of Ys I and II) and generally got consistent western releases from that point on.
I go back and forth whether Dawn of Ys or Ys Seven is my favorite. Ys V is definitely the worst one. I still need to play memories of celceta though.
Currently have the $100 limited edition of Ys VIII pre-ordered ---