Best way to detect touch on a GameObject

I think the best way to achieve this would be using Raycasting, for this Specifically Physics2D.Raycast().

I don't have access to Unity right now, but from memory you should try something like this:

 using UnityEngine;
 using System.Collections;
 
 public class RaycastTest : MonoBehaviour {
 
     Vector3 touchPosWorld;
 
     //Change me to change the touch phase used.
     TouchPhase touchPhase = TouchPhase.Ended;
 
     void Update() {
         //We check if we have more than one touch happening.
         //We also check if the first touches phase is Ended (that the finger was lifted)
         if (Input.touchCount > 0 && Input.GetTouch(0).phase == touchPhase) {
             //We transform the touch position into word space from screen space and store it.
             touchPosWorld = Camera.main.ScreenToWorldPoint(Input.GetTouch(0).position);
 
             Vector2 touchPosWorld2D = new Vector2(touchPosWorld.x, touchPosWorld.y);
 
             //We now raycast with this information. If we have hit something we can process it.
             RaycastHit2D hitInformation = Physics2D.Raycast(touchPosWorld2D, Camera.main.transform.forward);
 
             if (hitInformation.collider != null) {
                 //We should have hit something with a 2D Physics collider!
                 GameObject touchedObject = hitInformation.transform.gameObject;
                 //touchedObject should be the object someone touched.
                 Debug.Log("Touched " + touchedObject.transform.name);
             }
         }
     }
 }

Again please check this works, as i cannot at the current time of writing. You can change touchPhase to change the TouchPhase used to detect a touch, link to the doc for this Enum is here. Check the documentation for Input.GetTouch() for more examples and information on how to get and use Touches.

You probably want to modify this to check if a touch begins and ends on the same object, but this is a good starting point for basic functionality.

Hope this helps!

Maybe Try this:

 if (Input.touchCount == 1 && Input.GetTouch(0).phase == touchPhase) {
         Ray ray = Camera.main.ScreenPointToRay(Input.GetTouch(0).position);
         RaycastHit hit;

         Debug.DrawRay(ray.origin, ray.direction * 100, Color.yellow, 100f);

         if(Physics.Raycast(ray, out hit))
         {
             Debug.Log(hit.transform.name);
             if (hit.collider != null) {
                 
                 GameObject touchedObject = hit.transform.gameObject;
                 
                 Debug.Log("Touched " + touchedObject.transform.name);
             }
         }
  }

touchPhase is set to TouchPhase.Began

A combination from @rob5300 post and https://www.youtube.com/watch?v=0sFrDJKwsdM

better and easy way, just add box collider and a script with this event to your game object:

OnMouseUpAsButton() { }

will the debug for raycast touch position response if i use mouse to click on the object during the game view in unity? because I'm trying to test out whether the raycast by touch position is working or not.

 #if !UNITY_EDITOR
 if( Input.touchCount>0 )
 {
     foreach( Touch t in Input.touches )
     {
         Debug.LogError($"current touch {Input.touches}");
         Debug.LogError($"touch count is {Input.touchCount}");
         Vector3 touchPos = t.position;
         if( t.phase==TouchPhase.Began )
         {
             Ray ray = Camera.main.ScreenPointToRay( touchPos );
             RaycastHit2D hit = Physics2D.Raycast( ray.origin , ray.direction );
             if( hit.collider!=null && hit.transform==transform )
             {
                 Debug.Log($"Hit: {hit.transform.name}");
                 myOnMouseDown();
                 break;
             }
         }
     }
 }
 #endif