Correct spelling


Correct spelling, explanation: suing is the correct gerund form of the verb sue because in case the verb ends with a vowel e, it is omitted when adding the suffix -ing (with the exception of -ee, -ye, and -oe endings). So bakebaking, suesuing, etc. Therefore suing is the correct form and sueing is a mistake.

Definition of suing:
verb, gerund form of sue, to start legal proceedings with someone
Consumers suing companies are very often sighted in the USA.
Another option for Jim is suing his insurer for not meeting the agreement.

Incorrect spelling


Incorrect spelling, explanation: this form is a misspelling, because the root verb here is sue, so it ends with vowel e; in such case we skip it when adding -ing ending (suesuing). Therefore sueing is an incorrect spelling. The correct one should be suing.