Matching left and right single-quotes used as apostophes
The best way to handle your issue (and avoid SQL injection) is to pass in your user input as a variable.  Since you are using a LIKE you can do something like this:

CREATE TABLE #person (person_name nvarchar(50))
INSERT INTO #person VALUES (N'Bob'),(N'Bo''b'),(N'Bo‘b'),(N'Bo’b'),(N'Bo#b'),(N'Bo^b')

DECLARE @user_input nvarchar(50) = 'Bo’b'

SET @user_input = REPLACE(
                        REPLACE(
                                REPLACE(@user_input, N'‘', N''''), 
                                N'’', N''''), 
                                N'''', N'[‘’'']')

-- @user_input now == Bo[‘’']b

SELECT person_name
FROM #person
WHERE person_name LIKE @user_input


Basically this replaces all of the different 's with a single type (the ') and then puts []'s around all three so that they get used in the LIKE.