Ways to deploy code to production server (linux server) with jenkins ?

I'm not that familiar with JavaScript development, but this could do it for you:

node {
    stage("Checkout") {
        //checkout your app
    }

    stage("Build") {
        //Build your app
    }

    stage("Deployment") {
        sshPublisher(publishers: [
            sshPublisherDesc(configName: '', sshCredentials: [
                encryptedPassphrase: '{encrypted_ssh_passphrase}', 
                key: '', 
                keyPath: '', 
                username: 'user'
            ], 
            transfers: [
                sshTransfer(cleanRemote: false, 
                excludes: '', 
                execCommand: 'commandToExecuteAfterTransfer', 
                execTimeout: 120000, 
                flatten: false, 
                makeEmptyDirs: false, 
                noDefaultExcludes: false, 
                patternSeparator: '[, ]+', 
                remoteDirectory: 'remoteDirectoryOfYourServer', 
                remoteDirectorySDF: false, 
                removePrefix: '', 
                sourceFiles: 'pathToFilesToCopy/*')
            ], 
            usePromotionTimestamp: false, 
            useWorkspaceInPromotion: false, 
            verbose: false)
        ])
    }
}

This is done via the SSH-Publisher Plugin. Though I still do not recommend deploying via Jenkins, since the SSH and SCP Publisher Plugins are very old (2 and 10 years respectively) and may contain vulnerabilities.

Another approach would be this, which is marginally better, if your target-server supports it. This approach again, is not really recommendable either, since it requires NPM to be on a production machine, which is a bad idea tbh.

What I instead would recommend is, let Ansible or other tools take care of it.
Push your built code to a git repo and let ansible pull the production code. That way you don't need a compiler/interpreter on your prod machine. This could also be automated via jenkins easily, since it has ansible plugins that could run your playbooks after the production code is committed to git.

I love jenkins, but it's not the best tool for everything, unfortunately :D

It really depends on your environment and what you are doing and how. In my opinion in standard environments the first step is to contenerize the application during CI/CD.

You commit / release a tag and automatically you get a container. You run the unittest inside the container and the integration test against the container. If everything is green you deploy the new container.

But this is only one approach, whatever you decide to do, is important to make sure it works well also with the cloud provider you are using.

Without more information is hard to help...