Passing bash variable to jq

I resolved this issue by escaping the inner double quotes

projectID=$(cat file.json | jq -r ".resource[] | select(.username==\"$EMAILID\") | .id")

Consider also passing in the shell variable (EMAILID) as a jq variable (here also EMAILID, for the sake of illustration):

   projectID=$(jq -r --arg EMAILID "$EMAILID" '
        .resource[]
        | select(.username==$EMAILID) 
        | .id' file.json)

Postscript

For the record, another possibility would be to use jq's env function for accessing environment variables. For example, consider this sequence of bash commands:

[email protected]  # not exported
EMAILID="$EMAILID" jq -n 'env.EMAILID'

The output is a JSON string:

"[email protected]"