How to generate JWT token on JMETER using a RSA 256 private key Required library or jar file?

I believe you will need to go for Groovy scripting for this

1. Get a JWT client library, for instance this guy will be a good choice and drop it to JMeter Classpath (make sure to include all the dependencies)

2. Restart JMeter to pick up the .jar

3. Add JSR223 Sampler to your Test Plan

4. The example code would be something like:

   def keyPayr = io.jsonwebtoken.security.Keys.keyPairFor(io.jsonwebtoken.SignatureAlgorithm.RS256)
   
   def now = java.time.Instant.now()
   
   def clientId = 'foo'
   
   def jwt = io.jsonwebtoken.Jwts.builder()
           .setAudience('https://example.com')
           .setIssuedAt(Date.from(now))
           .setExpiration(Date.from(now.plus(5L, java.time.temporal.ChronoUnit.MINUTES)))
           .setIssuer(clientId)
           .setSubject(clientId)
           .setId(UUID.randomUUID().toString())
           .signWith(keyPayr.private)
           .compact()
   
   log.info('Token: ' + jwt)
   

Demo: