Correct spelling, explanation: supplement is the only correct spelling, because the English word supplement is based on a Latin word supplementum and the word did not change much after borrowing, besides losing the distinct Latin ending.

Definition of supplement:
Noun
1. A thing that is added to another thing in order to make it better or to make something complete.
I eat well but in the winter I take vitamin D supplement just to make sure I’m healthy.
2. An extra part of a book, paper, or magazine, containing additional information
The Sunday magazine always comes with a special comic supplement. I love it.
Verb
1. The act of adding something to another thing, to make it better, complete, or to reinforce something.
I’m not doing well financially, so I supplement my income with a side job.

Incorrect spelling, explanation: despite the fact that the pronunciation of a related word, supply, may suggest this spelling, supliment is not a correct word. The word has its roots it’s Latin, and based on that, the only correct spelling of this noun is supplement.

Incorrect spelling

Incorrect spelling

Incorrect spelling

Incorrect spelling

Incorrect spelling

Incorrect spelling