Query with the Objects and search with the content(definition) of the stored proc
select o.name as [StoredProc] from sys.objects o
inner join
sys.sql_modules m
on
o.object_id = m.object_id
where
m.definition like '%[String to be Searched]%'
or we can directly query into the Sys.Procedures
SELECT Name FROM sys.procedures
WHERE
OBJECT_DEFINITION(OBJECT_ID) LIKE '%
AND
OBJECT_DEFINITION(OBJECT_ID) LIKE '%