Does it give you what you are looking for?

DECLARE @t TABLE (a BIT, b BIT, c BIT)
INSERT INTO @t (a, b, c) SELECT 1, 0, 1
INSERT INTO @t (a, b, c) SELECT 1, 1, 1
INSERT INTO @t (a, b, c) SELECT 0, 0, 1
INSERT INTO @t (a, b, c) SELECT 1, 0, 0
INSERT INTO @t (a, b, c) SELECT 0, 1, 0
INSERT INTO @t (a, b, c) SELECT 0, 0, 1

DECLARE @a BIT, @b BIT, @c BIT

-- Try changing this to the desired combination
SELECT @a = 1, @b = 1, @c = 1

SELECT *
FROM @t
WHERE 
	(@a = 1 AND a = 1)
	OR
	(@b = 1 AND b = 1)
	OR
	(@c = 1 AND c = 1)

Hi Jacob Thanks for your reply

I need to get all the records if i pass @a=0 @b=0 and @c=0 irrespetive of condition. From the above query if i pass all zeros then i am not getting any rows.

How about this?

DECLARE @t TABLE (a BIT, b BIT, c BIT)
INSERT INTO @t (a, b, c) SELECT 1, 0, 1
INSERT INTO @t (a, b, c) SELECT 1, 1, 1
INSERT INTO @t (a, b, c) SELECT 0, 0, 1
INSERT INTO @t (a, b, c) SELECT 1, 0, 0
INSERT INTO @t (a, b, c) SELECT 0, 1, 0
INSERT INTO @t (a, b, c) SELECT 0, 0, 1

DECLARE @a BIT, @b BIT, @c BIT

-- Try changing this to the desired combination
SELECT @a = 0, @b = 0, @c = 0

SELECT *
FROM @t
WHERE 
	(@a = 0 OR a = @a)
	AND
	(@b = 0 OR b = @b)
	AND
	(@c = 0 OR c = @c)

If i keep AND there then the below scenarios wont work If i receive @a value as 1 then i need to retrieve records having a=1 records only if i receive @a=1,@c=0 and @b=1 then i need to retrieve records having a=1 or b=1 if i receive @a=1,@b=0 and @c=1 then i need to retrieve records having a=1 or c=1

Is it closer to what you are looking for?

DECLARE @t TABLE (a BIT, b BIT, c BIT)
INSERT INTO @t (a, b, c) SELECT 1, 0, 1
INSERT INTO @t (a, b, c) SELECT 1, 1, 1
INSERT INTO @t (a, b, c) SELECT 0, 0, 1
INSERT INTO @t (a, b, c) SELECT 1, 0, 0
INSERT INTO @t (a, b, c) SELECT 0, 1, 0
INSERT INTO @t (a, b, c) SELECT 0, 0, 1

DECLARE @a BIT, @b BIT, @c BIT

-- Try changing this to the desired combination
SELECT @a = 1, @b = 0, @c = 0

SELECT *
FROM @t
WHERE 
	(@a = 0 OR (@a = 1 AND a = @a))
	AND
	(@b = 0 OR (@b = 1 AND b = @b))
	AND
	(@c = 0 OR (@c = 1 AND c = @c))

If i am passing @a=1,@b=0 and @c=1 then i am expecting records like this a=1 or c=1 but i am getting like this a=1 and c=1

Try this query

SELECT *
FROM @t  WHERE 
a = CASE WHEN @a=1 OR ( @a=0 AND @b=0 AND @c=0) THEN 1 ELSE NULL END  OR 
b = CASE WHEN @b=1 OR ( @a=0 AND @b=0 AND @c=0) THEN 1 ELSE NULL END  OR 
c = CASE WHEN @c=1 OR ( @a=0 AND @b=0 AND @c=0) THEN 1 ELSE NULL END

Or Try Another Simplest

SELECT * FROM @t
WHERE (1= CASE WHEN @a=0 AND @b=0 AND @c=0 THEN 1 ELSE NULL END) OR
(a =    CASE WHEN @a=1 THEN 1 ELSE NULL END)  OR 
(b =    CASE WHEN @b=1 THEN 1 ELSE NULL END)  OR 
(c =    CASE WHEN @c=1 THEN 1 ELSE NULL END)

Thank you Mitesh, It is working.

Please Mark this as answer if it is working. so this question is closed.

good job mitesh!