My Redmi 1s has a battery capacity 2050mAh (BM41). And the upgrade of the phone is Redmi 2 with capacity 2200mAh(BM44).
Can I use this battery if it fits in my device? Will it creates any software problems?
Not Recommended in general
These stages are regulated and controlled by the the charging circuit in charger/ in device by firmware files to switch to various stages. Battery capacity is very much integral to this. By replacing with a battery of higher capacity (or extended battery unless OEM approved) charging may less than optimal and therefore the performance or life of battery could be affected
Edit: The number of terminals and purpose could also vary ( some batteries have three terminals and some have 4). This would be an issue
Your case: There is hardly a difference in mAh so it may not matter at all , if it fits- normally OEMs like Samsung make sure that the batteries cannot be interchanged between devices - can't say about Redmi. The benefit you would get is marginal, so would recommend playing safe and not replacing to avoid any problems