You can do this. That is, New York law allows tenants in common on property with ownership
interests stated on the deed.
For example, it is possible for a property to have two or more owners with their respective ownership listed on the deed.
Now, it is important to understand that once you make this transfer is considered a gift in non-revocable. The recipient of this gift would have the same ownership rights as you. And they could transfer those rights to another.
Also, if the value of this gift exceeds $13,000 you would owe a tax based on the US gift tax.
However, to answer the question, can you give your mother a 1% interest in the home that you own? The answer is yes.
1% would be the smallest percentage you could award.
Please let me know if you have more questions. Happy to help if I can.