I've seen this a lot in my tables: people start fidgeting, making jokes, doodling, playing with their phones because they get bored waiting for their turn or for something interesting to happen. One player even fell asleep during several sessions. I want to start out by pointing out that while ADHD definitely has played into it in some cases, it hasn't ever been the only reason in my (admittedly limited) experience. Also, without knowing your group, I can only rely on educated guesses: everything I say you should try out, but always with a grain of salt. There's no silver bullet that works for everyone.
Talk to your players
This is pretty much a given --- you need to establish why the player is acting zany during the game. It's pretty common for players to act this way simply because they're not engaged enough. Also try to determine, in a non-accusatory tone, what kind of game your players actually want to play. The Same Page Tool is a helpful resource for discussion (note that it's NOT a survey, it's a conversation starter!)
Consider a switch of system
The choice of system has a huge impact on the pacing. DnD tends to be very slow-paced because of the heavy, crunchy combat engine, which makes it a hard game for people who want situations to resolve more quickly. Many people try to cope with the occasional boredom in DnD because they don't know of the alternatives; for me, it's often turned out that a change of system can help deliver the experience the player wanted.
To illustrate the difference: a DnD session with a couple of combats usually gets you about the equivalent of a chapter in a book in three hours. Other systems can fit a whole book in that time, largely because less time is spent rolling stuff that doesn't substantially advance the scene (mostly combat encounters).
A straightforward alternative to try is Dungeon World, which is a relatively lightweight sword and sorcery fantasy game that tries to emulate the heroic fantasy feel of DnD. It is crafted for narrative experiences over strategy and realism. It doesn't have a tactical combat system, which necessitates a bit more improvisation from everyone (including the GM), but also makes action quite a lot quicker and ideally, more varied. You might also be interested in the setting-agnostic systems Fate Accelerated or a system built on Fate Core.
Split the party
Some people will just not enjoy playing together. If you have players who want a serious game and others who want a zany game, and you can't get them to flex on that, your best shot at keeping everyone playing is to split the group into two with different tones. It's more work for you, because you have to find more players and possibly run two games --- but you can save some effort by having someone else be the GM or using a system that requires less preparation than DnD (eg. the aforementioned Dungeon World) for one or both tables.
