You need to replace .. with ., or just reference client/ directly, also you will need to remove the asterisk:
"devStart": "nodemon --ignore ./client/ --exec babel-node src/server.js"
Or
"devStart": "nodemon --ignore client/ --exec babel-node src/server.js"
According to nodemon docs this is how to ignore a directory via command line:
nodemon --ignore lib/ --ignore tests/
Also note that nodemon will only restart the node process, if you change the npm script you will need to kill the process and re-run npm run devStart