Touchscreen for unity

One way to do this is to create 3DText GameObjects for the left, right and jump key. You will then need to give them BoxCollider components. Once this is done you need to Raycast a ray to the touch position and check if you've hit one of the 3DText's colliders. If you hit the left 3DText, then you simply move the character to the left and so on.

Have a look at this pseudo-code. I Hope it helps:

 public class PlayerController : MonoBevaviour
 {
     // Those 3 are the 3DTexts in the scene
     private GameObject leftArrow;
     private GameObject rightArrow;
     private GameObject jumpKey;
 
     private void Start()
     {
         // Find the 3DTexts in the scene
         // Another way will be to make the game objects public and drag and drop them from the editor
         this.leftArrow = GameObject.Find("Left Arrow"); // The name of the leftArrow 3DText is "Left Arrow"
         this.rightArrow = GameObject.Find("Right Arrow");
         this.jumpKey = GameObject.Find("Jump Key");
     }
 
     private void Update()
     {
         // If we have touched the screen
         if (Input.touchCount > 0)
         {
             foreach (var touch in Input.touches)
             {
                 // If the touch began, or moved, or is on the screen but stationary
                 if (touch.phase == TouchPhase.Began ||
                     touch.phase == TouchPhase.Moved ||
                     touch.phase == TouchPhase.Stationary)
                 {
                     Ray ray = Camera.main.ScreenPointToRay(touch.position);
                     RaycastHit hit;
 
                     float rayLength = 100.0f;
 
                     if (Physics.Raycast(ray, out hit, rayLength))
                     {
                         // If the ray hit the left arrow game object
                         if (hit.collider.gameObject == this.leftArrow)
                         {
                             // Move the player to the left
                         }
                         else if (hit.collider.gameObject == this.rightArrow)
                         {
                             // Move the player to the right
                         }
                         else if (hit.collider.gameObject == this.jumpKey)
                         {
                             // Make the player to jump
                         }
                     }
                 }
             }
         }
     }
 }

I'm a bit against using 3D text when possible as you get lots of extra draw calls. It really just needs a guitexture with a touch script. Or if you need a mesh, just a plane mesh with a script to always look towards the camera and a collider for ray casting.