Is there any method to handle mute or unmute using JTAPI library?

Or

Is there any other option to handle this mute or unmute in TSAPI function with respect to JTAPI?

Thre is no way to actually mute/unmute a phone as that is a local function of the phone.

However, it is possible to control the flow of media between parties in a call by using the Selective Listen Hold (SLH) feature. There is a full description of this in the TSAPI Programmers Guide and I think the correct JTAPI API for it is LucentV5TerminalConnection.listenHold().

A couple of warnings:
1. SLH requires there to be a TSAPI Advanced license in place.
2. SLH is a bit tricky to use. It blocks A from receiving B's media rather than blocking A from transmitting media. So, IIRC, if A, B & C are in a call and you want to mute A, you will need to SLH B from A and then SLH C from A.

Martin