The petition deadline for independent candidates, and the nominees of unqualified parties, for local office in New York state was May 25. One of the petitions was submitted for Thomas Downs, an 18-year-old running for Mayor of New York city. His ballot label is Future Party. He needed 3,750 signatures. See this story.
Although the 2020 session of the New York legislature increased the statewide petition from 15,000 to 45,000 signatures, it did not increase the local or district petitions. Furthermore in 2021 it passed a bill, cutting those petitions in half, for 2021 only.