Custom Shader Giving Unexpected token error for period ' . '

Here is your working shader :

 Shader ".ShaderLive/Fixed Unlit"
 {
   SubShader
   {
     Pass
     {
       CGPROGRAM
       #pragma vertex vert
       #pragma fragment frag
 
       #include "UnityCG.cginc"
 
       struct appdata 
       {
         float4 vertex : POSITION;
       };
 
       struct v2f 
       {
         float4 pos : SV_POSITION;
       };
 
       v2f vert(appdata IN) 
       {
         v2f OUT;
         OUT.pos = mul(UNITY_MATRIX_MVP, IN.vertex);
         return OUT;
       }
 
       fixed4 frag(v2f IN) :COLOR
       {
         return fixed4(1,0,0,1);
       }
 
       ENDCG
     }
   }
 }

You made 2 mistakes in your code.

The first one, if you use some variables defined in UnityCG you have to include the header

 #include "UnityCG.cginc"

And the second one

 v2f OUT.pos = mul(UNITY_SHADER_MVP, IN.vertex);

does not really make sense : declare a struct, then initialize it.

Also, I think you want to use UNITY_MATRIX_MVP and not UNITY_SHADER_MVP.

Have fun ;)