Property mod in bank

Yes they have every right in the property left as they are the survived legal heir even though you are paying the EMIs to the bank.

Its better file a petition for succession Certificate and take no objection from them that they have no objection if the property is transferred in your favour only.

It is believed that you are Hindu and your husband has not left any WILL.

The mother/spouse/children are ClassI legal heir(s) and shall share the estate equally amongst themselves.

The mother can relinquish her rights in your favor.

You can continue to pay the EMI.........................however if you concur to bank to pay the debt in writing then you have to.

Otherwise wife is not liable to pay debt of husband.

Since the house is mortgaged the bank is safe in such case of 'Secured debt'.

Think on all pros and cons and decide as suitable to you.

1) Your husband's mother, yourself (wife) and your children are only I Class Legal heirs 

2) so all the I Class Legalheirs are having equal right over the property 

3) if your mother in law ready to give Release deed in your favour the property become your (yourself and your children) absolute property .

4.)your father in law is not having any right over your husband's property.