Property in which both parties have no proof of ownership

Hi. I am a father of 2 kids, have lived in a house built on land owned by my partners mom. We have been live-in partners for more than 9 yrs and just recently built the house. Unfortunately we had issues in our relationship causing it to end on a sour note. She ran away and is now living with another man but wants me to vacate the house claiming she solely owns it. Both of us do not have any proof to show this but have shared the cost in building the said property with me having the bigger share. currently I am the only one living in the house. My question po is do i have at least a shred of claim to this or do i really have to leave the house anytime she demands it? I have recieved a demand letter to vacate the house within 5 days or face the legal cases as per this demand letter. I hope i am making sense i am doing my best to explain the situation as accurately as possible. I did not sign the demand letter and informed them that i will be seeking legal advise as i feel that it is quite unfair on my part. Hoping to get a response soon. Thank you.

You say "partner" so I suppouse you aren't married.

It's a mess when not having legal diocuments. PERHAPS you can get some. It depend of what will be legaly decided, but her case is much stronger than yours, because even if you have paid whole house it isn't on your land and no lease contract. Compare: Even if having a lease contract which ENDS, then the building will belong to the LAND owner.
Is the land titled?
If yes, that make your case weaker.
If you have paid the property tax and can prove it, that can support your side some.

Is the letter from a lawyer or from someone with legal rights to DECIDE (as court or Barangay Captain) or just from a lawyer?
(I guess it's just from a lawyer.) If so the case isn't decided yet.
In any case protest in WRITING saying you disagree.

If it isn't from a court, go to the barangay captain IF your partner push the case.
How long time was it since your partner left? Perhaps it can be solved by you become a couple again? That's the simplest solution