Recently, my Samsung cell phone has got some “memory card error”. So, in order to make it workable again, I just formatted the inner memory card there. But, I still have many newly taken photos stored inside it. Is it possible for me to restore all these erased photos back? What should I do to rescue them all back? Thank you in advance!

MMm not sure this will work but you can put the card in a tablet-pc or laptop whit sd card reader and then use this program paretologic data recovery (or some similar software more suited for sd cards).

Most importantly... immediately remove the card from your phone! Any writes to the card will corrupt any photos that may be there.

I'd try Recuva or PhotoRec to get back what you can. Both free, both very good.

Best of luck,
WallyH

Ok! Stop writing anything else on this formatted memory card in case of any data loss.
In your case, in order to get back your photos there, you need memory card data recovery tools like Recuva, 4Card Recovery, PhotoRec and more.
No matter which one you choose to use, you’d better act carefully in case of any unnecessary data loss.
Note: Never format a card or drive without data backups in the future.