My mother and I own a property since 1990. If she applies for Medicaid to pay for nursing home , what are the laws regarding

For the purposes of Medicaid - it's as if she owns the whole property. This is a rebuttable presumption - you would have to show that you contributed the entire purchase price to rebut it. Most transfers will be subject to a 5 year Medicaid penalty. Nursing home Medicaid planning is a complicated field, there are many ways of saving her assets and some transfers will not be penalized. You should consult an elder law attorney.

If you have lived with your mother and provided care for her during the two-year period before she entered a nursing home, transfer of ownership to you would be exempt for Medicaid purposes. You should consult with a Medicaid qualified attorney to help you with this.

If you own it as joint tenants with a right of survivorship and you are refusing to sell, then the house is not available for Medicaid purposes, and there will be no estate recovery because the house would pass to the other joint own by operation of law, and any Medicaid lien would be extinguished upon her death. If you are tenants-in-common, then the asset is still unavailable for Medicaid if you are unwilling to consent to selling the house, but Medicaid will place a lien against mom's 1/2 and/or recover against her estate.

There is a 5 year look back period. There is also a law under article 81 mental hygiene law call "SUBSTITUTED JUDGMENT" additionally if you lived with your mom for two years prior to her going into a nursing home and you are disabled, you can request a waiver

If you own the house as joint tenants with rights of survivorship, then the house is protected from a future Medicaid lien. Medicaid allows a person to own their home with a value of a little more then $800K. If her half is more then the $800K, only then would it effect her eligibility. If you own the house as joint tenants then she can still receive Medicaid, but you have to worry about an Medicaid Recovery Lien. Since you have been taking care of her the last two years, you can have her transfer her half to you and it would be an exempt transfer. You should speak to an Elder Law attorney who can handle the Medicaid application and planning for you.