This Albany Times-Union story says that some Democratic candidates running in the primary for Delegate to the local Judicial Nominating Convention have been removed from the ballot, not because their petitions are invalid, but because their political opponents believe that the challenged candidates would, if elected, vote at the convention for someone who may not be eligible.
New York state political parties choose candidates for Judge of the Supreme Court at nominating conventions. The state is divided into twelve Supreme Court districts. Each district elects its own justices. There are no direct primaries for nominating Supreme Court Justices. Instead, within each district, each party holds nominating conventions. But delegates to the nominating conventions are chosen in party primaries.
Petitioning for convention delegates is extremely difficult. Most of the time, the only delegates who qualify for the primary ballot are candidates backed by the party apparatus. In this case, a rebel slate of delegates managed to complete the petitions, only to be told that they can’t run in the primary because they supposedly will vote for a Supreme Court nominee at the convention who may or may not be qualified to run. The rebel delegate candidates have filed a lawsuit to regain a place on the ballot.
This situation is very analogous to matters involving the electoral college in U.S. presidential elections. In 2012, the Libertarian Party presidential elector candidates were removed from the Michigan general election ballot, on the basis that they were pledged to Gary Johnson, who was supposedly ineligible under Michigan law to run for President because he had already run in the February 2012 Republican presidential primary in Michigan.