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You may go to mediation regarding your child's custody.
As a mother, you automatically have parental responsibility over the child.
You may apply for leave to remain on the basis of being a parent of a British Citizen child as your visa on the basis of being a partner may be revoked if your relationship is over.
See here: https://www.gov.uk/uk-family-visa/parent
For child welfare issues, you may contact this charity: https://childlawadvice.org.uk/information-pages/parental-responsibility/
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