How to limit the movement to only move the z axis

How to limit my ai movement to move only on the z axis. Ive already tried freezing the rotation and position on it’s rigidbody but instead when i jump my ai also goes up with me on it’s position and slightly rotates towards me.

private void Update()
    {
        StopFollowing();

        Vector3 relativePos = target.position - transform.position;
        Quaternion rotation = Quaternion.LookRotation(relativePos);

        Quaternion current = transform.localRotation;

        transform.localRotation = Quaternion.Slerp(current, rotation, Time.deltaTime
            * LookSpeed);



    }
    // Update is called once per frame
    void followPlayer()
    {
        Vector3 pos = Vector3.MoveTowards(transform.position, target.position, speed * Time.deltaTime);
        rig.MovePosition(pos);
        
;
    }

>Solution :

Freezing the rigidbody will only affect physics (using AddForce or rb.velocity)

You are using MoveTowards (basically teleporting it ignoring physics)

But you can limit it to Z-Axis manually:

void followPlayer()
{
    Vector3 targetPos = target.position; // copy target Position
    targetPos.x = transform.position.x; // keep x
    targetPos.y = transform.position.y; // keep y
    Vector3 pos = Vector3.MoveTowards(transform.position, targetPos, speed * Time.deltaTime); // now only considers z-difference
    rig.MovePosition(pos);
}

You basically modify the target Position to be equal on the x and y axis, so that the MoveTowards only uses Z effectively.