I apologise for my delayed response. Unfortunately I did not realize that you had responded to my follow up question.
You may apply for permission to remain in the UK on the basis of being a parent of a British Child. I will provide you the guidance information below in the event you proceed with the application.
What is the most important thing to qualify for this visa is for you to demonstrate that you are no longer in a relationship with your partner. So, therefore, ideally you must have separated ( you do not have to be formally divorced to qualify) and no longer living together.
In addition to the above, you must also show that you have :
sole parental responsibility for the child
• direct access (in person) to the child, as agreed with the parent or carer with whom the child normally lives or as ordered by a court in the UK- in addition in such cases:
o the parent or carer with whom the child normally lives must be a British citizen in the UK or settled in the UK and not the partner of the applicant o the applicant must not be eligible to apply for entry clearance as a partner under Appendix FM
In all cases, the applicant must provide evidence that they are taking, and intend to continue to take, an active role in the child’s upbringing.
I hope this helps. Do let me know how I may be of further assistance. Kindly indicate whether you accept the answer given. You may do this by clicking on the stars at the top of the page.
All the best