The same guidance lists a $15 filing fee for a claim up to $1,000 and $20 for a claim over $1,000 up to $10,000. Rules elsewhere in New York may differ; do not treat NYC figures as statewide.
Source: NY Courts.
US small-claims procedure
New York City small claims: official starting point
New York State Unified Court System guidance says an eligible individual can sue in NYC Small Claims Court for up to $10,000.