Recently I bought a Portable battery charger which has a power ratings of 5.1V 2.1A.
My original sony mobile charger has a rating of 750mA current rating.
So is there a threat to my battery health if i use this portable battery?
is there any over current protection inside mobile phones to protect the battery?

But when i continuously used it for a couple of days, my battery seems to behave quite badly, switching off at 25 % battery and jumping from 80% to Full etc.

 

Welcome to AAC
Using that charger is not a threat if the voltage is same as Sony charger, but you battery is dying so replace it first

But first tell us the sony charger voltage. You have only told us the current rating (750mA)

 

You cannot "feed" too much current to something the phone will only draw what current it needs to charge the battery, you can only feed too much voltage. "2.1A" written on the portable charger is the capacity of the battery inside it and suggests that it has the ability to charge your phone nearly 3 times.

Also, sounds like you need a new phone battery