Incorrect spelling, explanation: this spelling is incorrect because we don’t exclude y when adding -ing suffix to a verb. We only do this with the vowel e (for example care → caring). Y however remains, so the correct form should be studying.

Correct spelling, explanation: when -ing ending is added to a verb that ends with y, this letter stays within the word. Thus study + ing is studying. Studing is incorrect, because y was omitted, and it shouldn’t be. E is the only vowel that we throw away when adding -ing suffix to a verb.

Definition of studying:
noun, an act of someone who learns
Studying maths is a nightmare for me!
Jack is a terrible lawyer. Studying economics would be a better choice for him.