The apartment that you own is an asset. It counts against the asset cap. If you sell it, the money that you make from the sale will also be an asset. Plus, the entire value of the real estate is counted as an asset, not just the part that you actually own.
The Marketing Handbook says:
B. PROPERTY OWNERSHIP
1. Asset Calculation
If an applicant owns any real property, the market value of that real property is
included in the calculation of household assets and is subject to the asset limit
(see Section 5-5.A, “Asset Limits”).
2. Income Calculation
If an applicant owns any real property, the actual or potential rental income from
that real property is included in the income calculation.
3. Prohibition – Rental Affordable Unit
For a rental affordable unit, no member of the applicant’s household may own
any residential real property in, or within a 100-mile radius of, New York City.
4. Prohibition – Homeownership Affordable Unit
For a homeownership affordable unit, no member of the applicant’s household
may own, or have previously purchased, any interest in residential
real property.
https://www1.nyc.gov/assets/hpd/down...dbook-8-21.pdf