Help please ... Urgent help needed

[Umi1]

I have been refused for student visa extension because of Toeic test ... And got a letter from ukba saying that to go for signature I am liable to detain :
I have girlfriend here she was on asylum before and now she has got refugee status and we were in relation ship when she had no status and now we have one daughter who Born after she got refugee status .. Could you please give me Advice .. Is there anyway that I could get stay on the basis of the child .. My name is not on her birth certificate

Please help me I have to put application this week
I don't know which one would be best and fast track

Waiting for your kind advice