Future Sued by Baby Mama Claiming He Made Threats to Coerce into Abortion

Future allegedly tried to smear his baby mama's name in an effort to make her look like a woman who sleeps around, and made threats in hopes of getting her to have an abortion ... so she claims in new legal docs.

Eliza Seraphin is countersuing the rapper claiming Future's made tons of false allegations against her including saying she sleeps around for financial gain, has a mental health disorder and calling her a "hoe" after he claimed she "stole my last name."

According to docs, obtained by TMZ, Eliza says Future sent her a text saying "let your lawyers speak for u at this point! u bogus, stole my last name now u want to b relevant jus fall back off the net trying to to prove a point."

She claims he also texted her, "TMZ this bitch stole my last name I think that's what i heard! I will never respect a clout chasing bitch NEVERRRRRRR FOH."

Eliza claims she and Future carried on a relationship for 2 years and engaged in unprotected sex during that time ... leading to the birth of their daughter. Earlier this month, the paternity suit was resolved when DNA results showed Future is the baby daddy.

Still, Eliza claims Future's made this a living hell for her ... claiming he continually made her out to be someone who sleeps around with various men in an attempt to get pregnant for her own personal financial gain.

And, get this ... Eliza claims Future's made various threats -- even allegedly threatening to have her killed -- while she was pregnant "in an attempt to coerce her to terminate her pregnancy." Eliza claims she took these threats seriously enough to report them to police.