I recently wanted to apply for a visa at the embassy when studying in the United States. My mother is abroad but is staying illegally. Will it affect my visa application?

It depends on whether your mother has dealt with the visa officer or the immigration bureau when she went out, and filled out an information form or something. If she has left relevant information, the US Immigration Service will find out, which will have a great impact on your visa. If not, it will not have a big impact on you and there is no need to tell the visa officer.