I am in no longer contact with the software contract company that has developed and deployed my mobile app to App store via their account. how do I gain ownership of the app? will the store allow me to develop and deploy the app under same name?
App transfer
If you have a contract with the developer, you should check what it says.
Do you have the source code, or access to it?
If the contract doesn't allow you access to the source code then you will have to develop the app from scratch, and you won't be able to use the same name.
If the contract allows you access to the source code, you need to get that source code.
If you get the source code, you need to contact Apple Developer Support (that "Support" link at the top of the page) showing them the contract, and they should be able to transfer the app to you.
There are lots of things to check and Developer Support will ask you to prove a few things, so be prepared. Ask what they require upfront.
If you were to redevelop, that could not be the same app, as it would be rejected as spam.