David Bruce called the woman “vile names” while demanding to see the six-month-old girl, on September 30, said prosecutor Donna Fawcett.
Another text said: “Trust me you want to watch yourself, duck. I’m going to take all your teeth out.”
His ex-partner told police she “was worried about him trying to get me through a third party” and said: “Since we split he has caused me to fear for my own safety.”
She ended their 16-month relationship, in April, because “he was volatile and they argued a lot,” said Mrs Fawcett.
On September 25, he became so annoyed he hurled his own phone at the wall in anger, but he contacted her five days later to hurl abuse from his sister’s phone.
Anita Pidcock, mitigating, said Bruce, a machinist who lost his job earlier in the year, became frustrated when he wasn’t allowed to see the little girl.
“This defendant will have to find a way to co-parent his child,” she said.
Probation officer Raqia Bano said: “He said he had no intention to carry out the threats. He has accepted the victim is in a new relationship.”
The court heard he had a conviction for battery against a previous partner in 2015. No restraining order was requested or made.
Bruce, 28, of Beacon Drive, admitted sending abusive and menacing messages, when he appeared at Mansfield Magistrates Court, on Wednesday.
He received an 18-month community order, with 60 hours of unpaid work, and 30 sessions of the building better relationships course.
He must pay £85 costs and an £85 government surcharge.