Months after a woman hit Paul Pierce with a paternity lawsuit ... she is now asking a court to make the NBA great pony up nearly $30K a month in child support.

In court documents, obtained by TMZ Sports, Princess Santiago claims Paul is the father of her newborn and is asking the judge to award her sole legal and physical custody, monthly child support in the amount of $29,811 and another $100K for her legal bills. She is also again requesting genetic testing to confirm that Paul is, in fact, the daddy.

On top of that, she wants Paul to pay one-half of all "reasonable expenses" relating to her pregnancy, birth, and post-birth expenses -- which she says totals $18,846.

In the papers, Santiago notes that Pierce was an NBA player from 1998 to 2017 and says he earned "approximately $195 million to $203 million in total NBA salary."

She added that Paul "has publicly stated that during his NBA career he made enough money from endorsements that he did not have to use his NBA salary to pay his expenses or generous expenditures on his family, romantic partners and family."

As we previously reported ... Santiago filed a paternity suit in California in January -- claiming that Pierce is the father of their then-unborn child.

"This isn't about drama or attention," Santiago said at the time.

We reached out to Pierce's attorney for comment ... so far, no word back.