remove first comma in string using sql

In SQL-Server you can do It in multiple ways.

You use STUFF in following:

SELECT col1, 
       STUFF(col2,1,1,'') as [Col Without First Comma]
FROM tbl
WHERE col2 LIKE ',%'

or you can use RIGHT

SELECT col1, 
       RIGHT(col2,LEN(col2)-1) as [Col Without First Comma]
FROM tbl
WHERE col2 LIKE ',%';

or you can use SUBSTRING

SELECT col1,
       SUBSTRING(col2, 2, 255) as [Col Without First Comma]
FROM tbl
WHERE col2 LIKE ',%';

UPDATE

As per your comment you can update in the same ways too:

Using SUBSTRING

UPDATE tbl
SET col2 = SUBSTRING(col2, 2, 255)
WHERE col2 LIKE ',%';

Or using RIGHT

UPDATE tbl 
SET col2 = RIGHT(col2,LEN(col2)-1) 
WHERE col2 LIKE ',%';

Or using STUFF

UPDATE tbl
SET col2 = STUFF(col2,1,1,'')
WHERE col2 LIKE ',%';

The following query should work:
It will update all the records in the column.

UPDATE table
SET col2 = CASE WHEN LEFT(col2 ,1) =',' THEN RIGHT(col2,LEN(col2)-1)
                    ELSE col2 END

UPDATE table
SET col2 =  case when charindex(',',col2,0) =1 then right(col2, len(col2)-1) else col2 end

USE [LIB]
CREATE FUNCTION [dbo].[trimChar]
(
    @p_string  varchar(max),
    @p_char varchar(1)
)
RETURNS varchar(max)
AS
BEGIN
   declare @l_string varchar(max) = @p_string
   -- lets do the front
   while SUBSTRING(@l_string,1,1) = @p_char
   begin
      set @l_string = substring(@l_string,2,len(@l_string))
   end

   -- lets do the back
   set @l_string = reverse(@l_string)
   while SUBSTRING(@l_string,1,1) = @p_char
   begin
      set @l_string = substring(@l_string,2,len(@l_string))
   end
   set @l_string = reverse(@l_string)

   return @l_string

END
GO