Unity 2d android game How to "freeze" position on Y axis

So i’m creating an android game in Unity version 2020.3.13f1.
I have a script so the player moves upwards immediately on start and then the player should move around and dodge obstacles and so on…
But i have a problem, i only want the player to be able to move on the X axis. The Y axis should be “locked” so he can’t move up and down by touching on the screen.
I can’t figure out how to code this correctly, it always ends up in a mess somehow…

Here is my move by touch code:

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class MoveByTouch : MonoBehaviour {

    // Update is called once per frame
    void Update()
    {

        if (Input.touchCount > 0)
        {
            Touch touch = Input.GetTouch(0);
            Vector3 touchPosition = Camera.main.ScreenToWorldPoint(touch.position);
            touchPosition.z = 0f;
            transform.position = touchPosition;
        }
    }
}

Here is your solution:

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class MoveByTouch : MonoBehaviour
{
    // Update is called once per frame
    void Update()
    {
        if (Input.touchCount > 0)
        {
            Touch touch = Input.GetTouch(0);
            Vector3 touchPosition = Camera.main.ScreenToWorldPoint(touch.position);
            transform.position = new Vector3(touchPosition.x, transform.position.y, 0);
        }
    }
}