Apple says "Your iOS Distribution Certificate expiring" what i need to do

It is just a reminder of the certificate that is going to be expired very soon in future.

I want to know what I need to do if I modify my existing app. Will I able to update in future the same app with new certificate and new profile.

Yes, You can always able to create new certificates (Some has limitation to create) and use these certificate to generate new mobile provisioning profile or regenerate mobile provisioning profile using the new certificates.

Using old certificate (Expired) you can not able to run build on device and not able to publish app on App Store.

The new certificate will not affect on your app. In simple words, certificates are being used to run app on device, publish app on App Store, push notification, etc.

As per new updates, you don't need to renew the certificate as a separate action. The renewal is based on the expiration of the Apple developer account. By taking the action of renewing your membership, this will automatically renew your certificates.