Human fighter found a useful way around the issue of having to hold a torch or find a torch-bearer. He wants to affix a device like a sconce to the front of his shield that will hold a torch in place.
I can't find any reason that you couldn't do this but would there be any consequences to this?
The hot part of the torch is going to have to be kept away from the shield; a wooden shield risks catching on fire, and a metal shield will simply transfer the heat to the character's arm. But having the torch stick way out from the shield makes it unwieldy and messes with its balance, making it very hard to use the shield to actually protect yourself. Alternately you could have the torch holder keep the burning part up above the rim of the shield, but then the torch will be directly in your line of sight when you're fighting, effectively ruining your field of view.
The whole point of a shield is to take hits so that they don't hurt you. It will likely only take one or two good hits to break the torch holder off of the shield.
Lantern shields are a thing that really did exist (though I understand that historians question whether they were actually used in combat), but it sounds like the player in question wants to just buy a basic shield and bolt a torch holder onto the front of it, which is an entirely different matter.
Anything you design to accommodate the torch will be subject to your own house rules, and is highly subjective and has many options. However, consider not giving it mechanical effects, and just narrating what seems appropriate.
Quick Examples:
Just keep in mind that a torch was designed to be a trade off for a weapon or shield, in dark areas. Another character could wield a torch, or cast a light spell on his shield. Or you could give him a magic item instead, that gives him a light effect, such as the Driftglobe.
Another alternative, making a torch in one hand and shield in the other not that bad, is to inform your player that they may use a torch as a weapon dealing the same damage as a club, or 1 fire damage.
Addressing #1 is largely a balance issue. Generally if a player is using a shield they are getting an AC boost at the expense of being able to use a 2nd weapon or use the hand for spellcasting (paladins have workarounds but that is part of their class features).
#2 is a far bigger issue simply because you will need to limit or balance this type of improvisation by all of your players against the game world. If a PC can do it any NPC should be able to as well.
I would handle #1 by making keeping the torch lit and in the bracket requiring concentration like a spell (the PC needs to hold his shield in a way that it lights the path, avoids burning himself, and avoids putting out the fire) and if they were hit or would otherwise need to make a concentration check they would need to do so to stop the torch from falling out onto the ground. That should keep the additional utility the PC has in balance.
As to larger system concerns if you allow players to modify items always introduce a risk or cost and it will help players specialize without gaining too much. Additionally there is probably a magic item that would give the shield bearing PC better vision or work like a torch that they could eventually get as well.
A better option might be to cast (or pay to have somebody cast) Continual Flame on the shield (or on a rivet that is then put in the center, etc). Sure, it can be dispelled, but it doesn't generate heat, and it can easily be covered to hide the light. Also, it could be made to look very cool.
The most obvious consequence would be increased weight of the shield, but there would also be the likelihood that the torch or its mount would be damaged by blows caught on the shield -- increasing repair costs (if you track such thing) and possibly dropping or extinguishing the light.
Another possible option, more expensive but perhaps more durable, would be to mount a lantern on the unexposed side of the shield, shining through a grating.
Presumably.
There's no rule against it, and it's easy to imagine several ways a normal human might accomplish that. If it's ad-hoc in the middle of a dungeon, I might ask for a Use Rope or Craft check, but it should be fairly trivial.
Failing that, fighter can just hold the torch in his shield hand. Most of what keeps a shield attached to your arm is the straps around your forearm. Holding the torch and the shield would be like holding two broomsticks in the same hand: slightly awkward at worst.
Ultimately, it sounds like the fighter is spending real effort and resources to duplicate the effects of a cantrip. Blocking that is unlikely to improve your game.
If an attack happens while it's in use, it's fairly likely to get knocked off, and pretty likely to go out in that instance.
It's also likely to unbalance the shield and make it less effective as a shield.
Consequences I would impose as a DM
I actually like this for town or city guards, because it's more important that they have a presence and see what's going on than actually fight in most instances, but for a constantly fighting PC, I don't see it being all that advantageous. As others have pointed out, there are lots of other magic work-arounds.
If it were my player I would allow it with the following restrictions...
I like the concentration check idea Joshua mentioned, so I would probably include that as well as disadvantage on any skill checks that involve a high degree of vision, dexterity, or physical exertion. (i.e. perception, investigate, acrobatics, athletics, or anything else that having the torch hanging there would make more challenging.)
I would also make note of the difference between the players ac with and without the shield, and say that any attack falling in that range has a potential to destroy or dislodge the torch. Not sure if I would assign it a hitpoint value and track damage on it, or a percentage chance with a dice check each time. I would probably negotiate with the player about it up front and then apply said rule whenever combat occurs.
