Why not build your api for free with express.js? and than push it to heroku or aws (amazon web service)? heck you could use aws api gateway or use expressjs with my current favorite serverless (aws lambda).
For working with expressjs, just google creating api's with express.js and tons of blogs and walk throughs to get up and running. Check out mern starter for api example or check out my repo (includes jwt auth with passport and bcrypt)
FYI with AWS free tier that expires after one year: Amazon API Gateway
AWS Free Tier (Non-expiring Offers) aka never expires: AWS Lambda