“Que + [verb]” is a form to give orders to no-one in particular/to everyone. It’s common language for kings, emperors, or anyone with high authority (so it’s pretty dated.)

Ex:

Que les jeux commencent !

Let the games begin!

Qu’on m’apporte à manger !

Bring me something to eat! (sort of)

Qu’on le jette aux lions !

Throw him in the lion pit!

So here it’s used ironically : you’re asking someone to say that you’re not a genius, if someone does it means they truly think that, and have the guts to say it to your face.

Note that the verb is in subjunctive (it doesn’t show for most of the verbs):

Que chacun prenne une arme !

Everybody, take a weapon!

Depends on context.

Possibility #1: imperative

Maybe you have learned that the imperative tense in French only exists for the second person singular, first person plural and second person plural. Well this is how the same meaning as the imperative (order, advice or suggestion) is formed for the third person singular or plural: que + sujet + verbe subjonctif.

For example :

Va-t-en ! Allons-nous en ! Allez-vous en !

Qu’il s’en aille ! Qu’elles s’en aillent !

With "on", it can be used to express a request without asking anyone in particular, as a master would ask in order to avoid addres. This is a bit snobbish and old-fashioned.

Qu’on nous apporte du champagne ! (= Apportez-nous du champagne !): Let us have some champagne!

In your example, it could be an order given as a dare:

Let someone dare to say that I’m not a genius! [and see what I will do to them]

Possibility #2: surprise, outrage, disbelief

But in other contexts, the same sentence and construction can be used to express surprise. For example :

Cette fripouille disait à qui voulait l’entendre que mes œuvres manquaient de créativité. Tu imagines ? Qu’on ose dire que je ne suis pas un génie !

In this context, it’s clear that the claim that the speaker isn’t a genius has already been made, and he/she is expressing outrage/disbelief at it.

Note that for the sentence in your example, in either of the cases, it sounds like someone is really getting on their high horse, so again depending on context it could also be meant sarcastically, which would negate the meaning. That would be my assumption if it was clear from context that the speaker didn’t really take themselves very seriously at all, e.g. if they were a comedian, but wanted to express mock outrage or pretentiousness.