In the past five years, the breakdown by league of players with an OPS (on-base count plus slugging percentage) above 1.000 is:
2023: (2) AL, (1) NL
2022: (2) AL
2021: (1) AL, (1) NL
2020: (4) NL
2019: (3) AL, (3) NL
Will resolve based on the number of hitters who meet the minimum plate appearances to qualify for OPS leaderboard on https://www.baseball-reference.com/ at the conclusion of the 2024 regular season.
This market does round up from 0.9995. If BBREF rounds up, this market will accept as a qualified 1.000 OPS.
Edit: something I did not address in writing this question is a midseason interleague trade. If a player is traded from an AL team to a NL team or vice versa, each set of statistics will be treated independently of one another, and if he fails to accumulate enough stats to qualify in either league, his total OPS will not count toward one or the other. See: Mark McGwire led MLB with 58 homeruns in 1997 but did not win the homerun title since he hit 34 HR with Oakland (AL) and 24 HR with St. Louis (NL).
According to Baseball Reference, there are currently two players qualified and above 1.000 OPS: Aaron Judge of the Yankees (1.114 OPS) and Shohei Ohtani of the Dodgers (1.036). I will follow with a separate market to cover specific players as they finish the season but keep this question open.
https://www.baseball-reference.com/leagues/majors/2024-batting-leaders.shtml