For parent partner route

[Hichamt15]

Hello

I have arrived to the UK late 2011 visitor visa I overstayed it then after 5 years I met a girl and decided to get married I went to the council and submitted the marriage application which was referred to the home office as I am an overstayed and she is British my application was refused by home office and was detained to be removed I have done some applications and was released on bail I was reporting once every 2 weeks awaiting answer to my partner application which was refused
My partner was pregnant and because of the refusal I stopped going to report

Now we have a baby 7 months old but we are not legally married she is a full time worker and I look after the baby as I don't work because I don't have the right to work

I want to put a new application to the home office but I am confused about what application I should use parent route or partner
Note my partner is living in a hostel now where I can't leave with her but I do have all the access to my son

Help please

[Casa]

FLR(FP) Parent route if you're living separately, but no guarantee of success. You'll need compelling evidence that you are taking part in your child's upbringing and as you're not married, you may have to take a DNA test to prove you are the child's father.

[Hichamt15]

Thanks for your reply

The baby has my name
Does that make it easier ?
Will it be more successful if we apply as we are living together ?

[Casa]

Thanks for your reply

The baby has my name
Does that make it easier ? No.
Will it be more successful if we apply as we are living together ? Possibly, but it would then be a FLR(FP) Partner route application.