Hi there and thank you for your question,
There is no legal basis that your ex-partner (the child's father) can simply take the child away from you. He can threaten all he wants, only a Court can order that the child be placed in the father's care.
Having said that, you can't simply walk away. The child's father has certain rights of access that you can't deny. The court could order a paternity test if there is a dispute as to who the father is.
What you need to do is to document in writing every threat that he makes against you, and keep every email, etc.
Don't give in to his demands. Let him go to Court to get access rights.
My advice is to write a letter to him to explain that you will not be bullied, and that he can't threaten you, and that if he wants access rights he will need to go to Court to gain suitable rights, and also that he will need to pay maintenance for the child.
If you REALLY think that it is not his child, then you should suggest a paternity test. If you deny the test, then you are essentially admitting that it is his child.
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Good luck and best regards,
Please note: This answer does not create an attorney-client relationship. Please consult a local attorney in person for legal advice. This information is being provided so you can better discuss legal matters with your attorney.