The T-60 pistol, first introduced to the series during Season 1 of the Fallout show and then added to Fallout Shelter is a modified Deagle from the orginal games redesigned to fit in more with the game's new style.

However, to make a possible to get a mod for this for Fallout 4, we need a full concept art-work system with modifcations, stats, etc. so here I am, translating it to a more conjustable version in a form of plain concept artwork.

Modifications:
[Standard Issue Receiver] - The basic modification of the weapon and the most common to be found on randomly generated loot, this provides the base damage, base recoil, and requires .50 cal rounds.
[Light Frame Receiver] - A lighter framed receiver, which is quite cheap to manufacture and reduces the overall weight of the weapon at the cost of a damage reducution, value, and a minor increase of recoil. Requires: .50 cal rounds.
[5.56 Conversion Receiver] - A converted receiver changing the ammo type to a weaker but more common 5.56 rounds. Reducing the damage slightly but decreasing the recoil a LOT.
[Hair-Trigger Receiver] - A version of the basic receiver with a faster fire-rate changing the fire-rate from 50 a second (without registering reload time) to as fast as the player can click. Reducing the damage to the same as the light frame. Requiring: .50 cal rounds.
[Auto Receiver] - A very overkill receiver, turning it from a slow-firing hand-cannon to a "and you're not out of ammo" gun within a few seconds. Increasing the recoil and reducing the damage a LOT. Requests .50 cal rounds.
[Hardened Receiver] - A heavier and more powerful receiver. This increases the damage at cost of a heavier weight and slight increase to recoil. Still requiring .50 cal rounds
[Powerful Receiver] The strongest varient of the gun. More than doubling the base damage. It is also extremely expensive and cannot be found on any randomly generated gun. It adds 5lb to the weight alone compared to the previous receiver. Requires .50 cal rounds.

[No Sights] - Completely removes the sights on the gun and reduces the weight ever so slightly.
[Iron Sights] - Equips the Iron-sights to the T-60 pistol. This is the base attachment to the weapon, found on most random spawns.

[Standard Issue Grip] - The base grip found on the side-arm, this weighs the least and has very minor edits, only making hits in V.A.T.s 10% cheaper.
[Survivor's Grip] - The grip equipped on the example gun in the middle. This is the survivor's grip, a cut and carved grip made of wood and light metals. A good pick for Wastelanders for its cheap price and good strength. Giving an increase to accuracy while aiming and reduces sway.
[Wooden Grip] - A pre-war grip used by military officers in high places. Its a stylish and pretty grip with a bit of sweat resistence to the wood hard to acquire with more cloth materials. Making it faster to holster/swap to and increasing hip-fire accuracy by 50%
[Comfort Grip] - Another wonderful grip, for a different reasons, the dark cloth material wrapped around the grip is very comfortable for the user with slots for each finger to slide in perfectly without them needing to touch. This improves aim-down sight accuracy, hit-fire accuracy, and fire-rate but costs the most adhesive and weighs the most.

[Standard Issue Barrel] - The lightest and cheapest to manufacture barrel on the pistol. This drastically decreases the armor piercing ability of the pistol but comes with the benefits of being much more light-weight and slightly higher damage.
[Vented Barrel] - Another cut barrel, this one comes with the benefit of reducing the heat your weapon produces when fired, letting you fire slightly faster without worry of overheating but dealing ever so slightly less damage but still less weight than the heavier barrels.
[Heavy Barrel] - A barrel with a built in compressor and designed for Anti-armor rounds. Letting all damage done by the pistol to ignore 50% of armor that the target has. This modification greatly increases heat build-up making less rounds be fired before overheating.
[Recoil-les Barrel] - A standard issue modification to the hand-cannon. This one removes 75% of all recoil produced by this weapon and slightly reducing heat-build-up of the weapon. But doubles the weight of the gun

That is all the modifications included to this weapon, however there is one more gun in this image you may have noticed. That is a one-o'-a-kind legendary weapon "Sawyer's Peace". Once a weapon of an Enclave Remnant soldier turned Minutemen. It is a modified and personally engraved T-60 Hand-Cannon. With a wrapped grip for max comfort and recoil-less barrel for precision aim. It includes a custom Legendary Effect:
Strength of the Minutemen: "this weapon gains an increase of damage depending on how far you are in the Minutemen Questline"