mouse hit doesn't shoot at the mouse?

I've kinda re-written part of the code but if i got you correctly you want something to shoot from your player and head towards the mouse hit?

if so you need to change the script to the following:

LocalScript!

local Player = game.Players.LocalPlayer
local Char = Player.Character or Player.CharacterAdded:wait()

local Speed = 50
local Mouse = Player:GetMouse()


-- dont actually need this function this is just my way to get the base where you fire a ball from as in Character.Torso if that doesn't exist then it will warn you that it doesn't exist and return the humanoidrootpart as default!.
function GetBasePartFromRig(char,SubPart)
    local humanoid = char:WaitForChild("Humanoid")
    SubPart = SubPart == nil and "HumanoidRootPart" or SubPart
    if(humanoid ~= nil) then
        local Base = nil
        Base = char:FindFirstChild(SubPart)
        if(Base ~= nil) then
            return Base
        else
            warn("Warning! SubPart of Character named "..tostring(SubPart).." has not been found! \n returning HumanoidRootPart as default!")
            return char:WaitFirChild("HumanoidRootPart")
        end
    end
    error("Error!: Humanoid is not a valid part inside "..tostring(char).." \n stopping script!")
end
local Base = GetBasePartFromRig(Char,"RightHand")


Mouse.Button1Down:connect(function() 
    --// just overridden with a part since i dont have what you have inside your script!
    local baconflake = (function() 
        local Part = Instance.new("Part",workspace) 
        for k,v in pairs(Enum.NormalId:GetEnumItems()) do 
            Part[v.Name.."Surface"] = Enum.SurfaceType.SmoothNoOutlines 
        end 
        Part.Size = Vector3.new(1,1,1) 
        Part.Shape = Enum.PartType.Ball 
        Part.Color = Color3.fromHSV(math.random(),1,1)
        return Part 
    end)()

    local aaa = Instance.new("BodyVelocity")
    baconflake.Anchored = false
    baconflake.CFrame = Base.CFrame
    baconflake.Parent = workspace
    aaa.MaxForce = Vector3.new(math.huge,math.huge,math.huge)
    aaa.Velocity = (Mouse.hit.Position - Base.CFrame.Position).unit * Speed
    aaa.Parent = baconflake

end)

the script is working as is.i've included a small function that will return the HumanoidRootPart as default if the part you specify doesn't exist inside the character..

as for the near to the player spawning you need the Vector3:Normal between the part your firing from and the mouse.hit.position Basically its the direction your pointing... In code this would be:

local LookDir = (Mouse.hit.Position - FirePoint.Position).unit
local Speed = 50

--// to fire somthing at 50 studs away from you towards  your mouse pointer simply do this

local Velocity = LookDir * Speed

--// now just apply that Velocity to a part and BAM you've got a part moving away from you, assuming you spawned it at your FirePoint. If its not then it will try to get to the `mouse.hit.p` but it will be offset by where you spawned your part.


local Spawned_part = Vector3.new(0,0,3)
local FirePoint = Vector3.new(0,0,0)
local MouseHit =  Vector3.new(0,20,0)

Spawn part will get to the position Spawned Point + MouseHit and that would be

local SpawnedPart_Goal = Vector3.new(0,20,3) -- or close to!

hope this helps!