So I'm playing a Way of the Kensei Monk, where I have chosen longswords and javelins as my Kensei weapons. I plan on using mainly my longswords, and drawing a javelins to throw when I need a little extra range.

My question is this: if I make an attack with the longsword, then throw a javelin as a part of my extra attack feature, does this count as two weapon fighting? Would I get my Dexterity modifier to the damage of the javelin throw?

I think that I would get my modifier to damage, since I am using the extra attack feature to attack with a monk weapon. The fact that it happens to be in my other hand shouldn't matter. I don't know if there is an official ruling on this though, so I wanted to check here.

If you are using Extra Attack to make the second attack, you are not using Two-weapon fighting.

So filcat's answer is absolutely correct... but the fact that you're dragging monk weapons and kensei into this makes me wonder whether you're asking something else, so I'll go ahead and beat a dead horse.

When using the "Two-Weapon Fighting" bonus action, ordinarily "You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative." Monk weapons allow you to "use Dexterity instead of Strength for the attack and damage rolls" instead of always-strength for melee and always-dex for ranged as normal... but that isn't to say that you're allowed to add a dex modifier to rolls that would not normally use a stat modifier at all like a Two-Weapon Fighting bonus attack.

So you're a Kensei monk, wielding a Kensei weapon (longsword) in one hand, and a Kensei weapon (javelin) in the other. To attack with both in a round...

1) You performed a regular attack with the longsword using an attack action, and want to use the "Two-Weapon Fighting" bonus action to throw the javelin. Ordinarily this is not possible, because javelins and longswords are not "light" weapons... but with the Dual Wielder feat it would be, as that removes the "light" requirement. Either or both attack can be thrown, so there's no problem there. But nothing about Dual Wielder removes the rule that you don't apply a stat bonus on the Two-Weapon Fighting bonus attack, so it's just a straight roll of your martial arts damage die.

2) You performed a regular attack with the longsword using an attack action, and want to use monk's martial arts ability to perform a bonus action attack. Unfortunately, martial arts specifically requires that that bonus action attack use an unarmed strike, not any monk weapon, so throwing the javelin is out. (same thing for the closely related "Flurry of Blows" using a ki point).

3) You're level 5+, and you made your first of two attack action attacks using the longsword, and your second of two attack action attacks using the javelin. As filcat mentioned, nothing about this situation involves a "Two-Weapon Fighting" bonus action, and so both attacks add stat modifiers as normal, and it doesn't take Dual Wielder to be able to wield both of these weapons. However, if you did have Dual Wielder, you could now follow up that javelin throw with a second sword swing or javelin throw (drawing a new javelin as part of the attack for free) that would not add stat modifier.

Thanks for the answers guys!

Chicken_Champ, I realize the question was worded pretty poorly. Your 3rd scenario is what I was asking about. The real confusion for me came from the idea that normally when you use the Extra Attack feature, you use the same weapon for both attacks. This kind of gave me the idea that any time you wanted to use two weapons to fight, it had to fall under the "two-weapon fighting" umbrella. 

Your explanation got those cogs working in my head though, and it makes sense to me now. Thank you again!