I have an interface as follows,
public interface MethodExecutor {
    <T> List<T> execute(List<?> facts, Class<T> type) throws Exception;
}
Also, I have a generic implementation like below,
public class DefaultMetodExecutor implements MethodExecutor {
   public <T> List<T> execute(List<?> facts, Class<T> type) throws Exception
   {
     List<T> result = null;
      //some implementation
      return result;
  }
}
Upto this there is no compilation issues,
But a specific implementation of this interface fails to compile, The one which shown below.
public class SpecificMetodExecutor implements MethodExecutor {
   public <Model1> List<Model1> execute(List<Model2> facts, Class<Model1> type) throws Exception
   {
     List<Model1> result = null;
     //some implementation specific to Model1 and Model2
      return result;
  } 
}
How can I implement this interface for some of the defined objects? Do I need to go for class level generics?
You need to make T a class type parameter, not a method type parameter.  You can't override a generic method with a non-generic method.  
public interface MethodExecutor<T> {
    List<T> execute(List<?> facts, Class<T> type) throws Exception;
}
public class DefaultMethodExecutor implements MethodExecutor<Model1> {
    public List<Model1> execute(List<?> facts, Class<Model1> type) throws Exception
    {
       //...
    }
} 
If the element type of facts should be configurable for a specific implementation, you need to make that a parameter too.
public interface MethodExecutor<T, F> {
    List<T> execute(List<? extends F> facts, Class<T> type) throws Exception;
}
                        You need to move your generic parameter types from method declaration to interface declaration, so you can parametrize specific implementations:
public interface MethodExecutor<T> {
    List<T> execute(List<?> facts, Class<T> type) throws Exception;
}
public class SpecificMetodExecutor implements MethodExecutor<Model1> {
    public List<Model1> execute(List<Model2> facts, Class<Model1> type) throws Exception {
        ...
    }
}
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