There is nothing that indicates paralysis changes the rules for suffocation.
Nothing in the description of the paralyzed condition indicates any change to or interaction with the rules for suffocation. So there is no change or interaction. Follow the suffocation rules as written:
A creature can hold its breath for a number of minutes equal to 1 + its Constitution modifier (minimum of 30 seconds).
When a creature runs out of breath or is choking, it can survive for a number of rounds equal to its Constitution modifier (minimum of 1 round). At the start of its next turn, it drops to 0 hit points and is dying, and it can't regain hit points or be stabilized until it can breathe again.
Obviously, being paralyzed will greatly compromise a creature’s ability to stop suffocating since they can’t move, but the condition does what it says it does; we don’t need to make it worse by inferring further effects that aren’t stated.