Set depth value in fragment shader

Question

I'm making a simple 2D renderer and I want to avoid redrawing as much as possible. My Vertex layout has the 2d position and a float depth value.

I want to assign a depth value to each of them after ordering to render them using depth testing and avoid overdraw.

So it will be like this:

1. Order all the sprites to draw by Y order. (isometric game)
2. Set a depth value to each of them (like an incrementing int)
3. Render them.

How can I achieve that?

I read something about gl_FragDepth but I don't know the range of values that I have to set there. Is it from 0 to 1?

These are my vertex/fragment shaders:

#version 330
layout(location=0) in vec2 v_position;
layout(location=1) in vec4 v_color;
layout(location=2) in vec2 v_texcoord;
layout(location=3) in float v_depth;
out vec4 color;
out vec2 uv;
flat out float depth;
void main() {
  gl_Position = vec4(v_position,0,1);
  color = v_color;
  depth = v_depth;
  uv = v_texcoord;
}

#version 330
uniform sampler2D tex0;
flat in float depth;
in vec4 color;
in vec2 uv;
out vec4 out_color;
void main() {
   gl_FragDepth = depth;
   out_color = texture(tex0, uv) * color;
}