Syntax: cat <filename> | jq -c '.[] | select( .<key> | contains("<value>"))'
Example: To get json record having _id equal 611
cat my.json | jq -c '.[] | select( ._id | contains(611))'
Remember: if JSON value has no double quotes (eg. for numeric) to do not supply in filter i.e. in contains(611)
To get an array back and persist it to a file, I wrapped the whole expression in an array like this:
cat input.json | jq '[ .[] | select( .field | contains("something")) ]' > output.json