Non Molestation ending/Access concerns

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I split from a violent/abuse relationship 13mths ago, and my ex last saw our child 13mths ago. She is now 4yrs old and will be 5yrs old when the Non Molestation order ends - unless hes successful at contesting it, which hes been contesting for 6mths.

My ex mentioned that in May 2017 at the contesting hearing to my solicitor (my attendance was excused) in the waiting room that I was only doing this non mol order to stop him having access and that it wont stop him applying, as hes already made an application for access. My solicitor (he was standing in for my usual solicitor) then said, what if shes not your child though? As it was mentioned to my usual solicitor in my statement, that my ex did question paternity whilst being in the relationship and accuse me of cheating a number of times. She might get a DNA? My ex just replied, if shes not my child I will simply walk away.

My ex in the last court hearing, 26 June 2018 which I attended, put in his statement to my allegations 'he made no financial contributions whilst living in my house and didnt help towards our childs clothing/shoes etc' - his response 'I dont pay child maintenance anymore, after I was told shes not my child' and 'I now know she did cheat on me'.

My concern is, after the non molestation runs out, it will be 2yrs since he last saw his child. If he then applies for contact, will all the background be taken into account? The fact a non molestation was granted? and the abuse/violence? or will they just allow him access and say theres no non mol now, so he can just come to your home and see his child?

I forgot to add that the non molestation order was taken out 7mths after our relationship ended, he made no attempt to see his child or make any arrangements. Instead, he would ring me and be emotionally abusive and then throw in that I am stopping him having access. I told him to go through the courts - which he didnt, he just continued harassing me, hence the non mol.

Recently been through the process of non molestation order with my ex.
I have contacted social services myself and supplied them with evidence of why I have stopped access. They were really helpful and I received a letter to say that they had evidenced my claims and would sudjest I ceased contact.
Social services aren’t the big scary people they are made out to be, and hopefully they could help you in regards to the possible contact.

Of course they will take into account background and if you’ve been granted the non mol it will go in your favour regarding contact.
Stay strong x