I could see this being useful if a pally is duel wielding. With or without multi classing. 

I don't think 1d4 only for self is worth holding it.

Does this apply to all weapons, even if said weapon deals a different type of damage?

Compare this to Hunter’s Mark, but without needing to swap targets.

from experience, it's absolutely useful for a dual-wielding paladin, especially since you can still add smite with this active for even more damage

you need to be able to make 4 attacks before this is equivalent to a smite and it uses your concentration. 

Quote from Mithise >>

you need to be able to make 4 attacks before this is equivalent to a smite and it uses your concentration. 

Assuming you can maintain concentration this spell will equal a smith in two or three turns and in a long combat with be work 3 first level smite.

Now, where it does get it's strength is with a weapon like a scimitar of speed, or that you can add radiant damage to ranged attacks. 

It has some nice uses, but it also has some solid competition.

I think the point is it works with weapon attacks, not just melee Weapon attacks, so works on ranged weapon attacks.  

Have a ranger/ war priest in party, not sure he has noticed the spell yet....

As others have noted there are better options for spell slots in most cases in terms of raw DPS.  Where this spell shines (get it) is when you're fighting undead.

Quote from LongrodThunderpump >>

As others have noted there are better options for spell slots in most cases in terms of raw DPS.  Where this spell shines (get it) is when you're fighting undead.

 That's not true in some ways because the highest competition for this spell, divine smite, gets more effective against undead. This is only better than divine smite against undead if they're too swarmy and divine smite will waste damage. It can finish off weakened zombies, but a divine smite can obliterate one with full health. And if it's a war domain cleric they have plenty of other options against undead.
The thing I'm most disappointed about is the lack of upcasting. 

This main benefit of this spell over Divine Smite is that it is usable with ranged attacks, while Divine Smite is not. Very handy for Dex-based paladins, and moreover if you fight from a distance you are more likely to maintain your concentration. Dual wielding doesn't work very well with it, since it uses your bonus action and you won't be able to dual wield until next round. On the other hand, dual wielding is great with with Improved Divine Smite gained at level 11.

It is also worth it if you happen to have a spellcaster that can cast Haste on you, so that with 3 attacks on a round you can inflict up to 3d4 extra damage each round, on top of your smites. That, and the +2 AC helps you maintaining your concentration.

Look! Hex, but worse in every possible way!

Could this be paired with Find Steed? This is from the Find Steed description:
"...While mounted on your steed, you can make any spell you cast that targets only you also target your steed."

So you AND your steed are doing Divine mini-Smites for a whole minute? Thought that would be a cool combo. 

Note: this spell may have it’s biggest competition for Spell Slots in Divine Smite, but there’s no competition between the two in terms of Action Economy.

This spell really should have been concentration free and only on melee weapon attacks. It would curb the optimal use being for ranged weapons while also enabling melee paladins this spell was clearly meant for to actually hold it for long enough to always beat smite overall. Its already weaker than Hunter's mark so this change is justified. That said I do love this spell even if its poorly implemented.

That combo is RAW legal though I'm sure it isn't supposed to be (why do all the more logical interactions have to be illegal while the more quirky ones are haha). I love this idea!

People seem to missing that fact that you could make a Spell Scroll for your ranger buddy. It would only take a day and 25gp to make. Now, your ranger buddy has and extra 1d4. And if they're at lvl5, that's 2 attacks per action. So, assuming they have a longbow, that's 2d8+dex plus 2d4 of radiant damage. Also, if they have Colossus Slayer - that's another 1d8. Also also, if they cast Hail of Thorns - that's another 1d10. All in 1 turn.

Quote from The12Brave >>

People seem to missing that fact that you could make a Spell Scroll for your ranger buddy. It would only take a day and 25gp to make. Now, your ranger buddy has and extra 1d4. And if they're at lvl5, that's 2 attacks per action. So, assuming they have a longbow, that's 2d8+dex plus 2d4 of radiant damage. Also, if they have Colossus Slayer - that's another 1d8. Also also, if they cast Hail of Thorns - that's another 1d10. All in 1 turn.

 A ranger cannot cast this spell scroll, as it's not on their ranger spell list, but they can with the Spellwrought tattoo. Costs more to make, but 1st level spells are cheap.

I wish it did something with up casting, increasing duration, apply to other creatures bigger die, just something.

Get it on your Monk with a war cleric dip, maybe? Sacrifice one bonus action to add 3 or 4d4 per round for the duration. One level of monk progression lost for this, martial weapons (dedicated weapon), and 1st level cleric spells for added versatility might be worth it?

Grab a whip, dedicated weapon, it'll use your martial arts die instead of the 1d4. Now you have a reach option. Might be something there. It's nice because the monk needs it's bonus actions, so moving hex or hunters mark is costly. This does a smaller die, but without needing to be moved around.

I've never used it on my paladin, though.