Correct spelling, explanation: suppresses is a third-person singular verb. Suppress is what the infinitive looks like. It originates from the Latin suppress- (meaning pressed down). As you can see, both in the basic form and in the source version, the word contains two double letters: -p and -s. We can’t change its construction when we conjugate this verb. The only correct form is suppresses, not supresses.

Definition of suppresses:
verb (third person), to end something by force
Mark always suppresses his laugh when he’s with his father.
A good medicine suppresses every symptom of illness.

Collocations with suppresses:
Some most commonly used collocations include: bloodily suppressed, systematically and violently suppressed.
Each rebellion was bloodily suppressed by the central authorities.
Students organizing dissent are systematically and violently suppressed.

Incorrect spelling, explanation: the word supresses is just a mistake because this version lacks one of the consonants: the second -p letter, which is necessary for this verb. The correct form, suppresses, consists of two parts: the root (suppress) and the regular -es suffix. The third person singular in the simple present tense always ends in -s or -es. Always remember that this verb must be spelled with two double consonants.