Correct spelling, explanation: stuck is a past tense of the verb stick. It’s an irregular verb, meaning it’s not created by adding an -ed suffix at the end, but that the word has a distinct past form.

Definition of stuck:
noun, past participle of stick
1. to insert or push an object into another object
The cat stuck its paw into the cream of the cake and licked it.
2. to be in a tight place unable to move
It turned out my leg was completely stuck between the rocks.
3. To be friends, to be in a group with someone (usually: stuck together with)
I and Angela have stuck together for most of our lives.

Idioms and phrases with stuck:
To be stuck in the past – to still live by the events that happen in the past and be unable to move on.
We all told Pamela that she should find a new boyfriend but she seems to be stuck in the past.
To get stuck into something – to be invested and enthusiastic about doing something.
Upon trying, I immediately got stuck into card tricks and spent hours practicing.

Incorrect spelling, explanation: stucked is incorrect, as it would be double past tense, or, in other words: it would suggest that stuck is a present form of the word, which is simply not true, as the present form here is to stick. What is more, stuck is an irregular verb, which means there is no -ed added, as the word has an already established past form.

Incorrect spelling

Incorrect spelling