Create a custom JSchemaGenerationProvider

public class User
{
    public int Id { get; set; }
    public string Name { get; set; }
    public DateTime CreatedDate { get; set; }
}

public class FormatSchemaProvider : JSchemaGenerationProvider
{
    public override JSchema GetSchema(JSchemaTypeGenerationContext context)
    {
        // customize the generated schema for these types to have a format
        if (context.ObjectType == typeof(int))
        {
            return CreateSchemaWithFormat(context.ObjectType, context.Required, "int32");
        }
        if (context.ObjectType == typeof(long))
        {
            return CreateSchemaWithFormat(context.ObjectType, context.Required, "int64");
        }
        if (context.ObjectType == typeof(float))
        {
            return CreateSchemaWithFormat(context.ObjectType, context.Required, "float");
        }
        if (context.ObjectType == typeof(double))
        {
            return CreateSchemaWithFormat(context.ObjectType, context.Required, "double");
        }
        if (context.ObjectType == typeof(byte))
        {
            return CreateSchemaWithFormat(context.ObjectType, context.Required, "byte");
        }
        if (context.ObjectType == typeof(DateTime) || context.ObjectType == typeof(DateTimeOffset))
        {
            return CreateSchemaWithFormat(context.ObjectType, context.Required, "date-time");
        }

        // use default schema generation for all other types
        return null;
    }

    private JSchema CreateSchemaWithFormat(Type type, Required required, string format)
    {
        JSchemaGenerator generator = new JSchemaGenerator();
        JSchema schema = generator.Generate(type, required != Required.Always);
        schema.Format = format;

        return schema;
    }
}

JSchemaGenerator generator = new JSchemaGenerator();
generator.GenerationProviders.Add(new FormatSchemaProvider());

JSchema schema = generator.Generate(typeof(User));
// {
//   "type": "object",
//   "properties": {
//     "Id": {
//       "type": "integer",
//       "format": "int32"
//     },
//     "Name": {
//       "type": [
//         "string",
//         "null"
//       ]
//     },
//     "CreatedDate": {
//       "type": "string",
//       "format": "date-time"
//     }
//   },
//   "required": [
//     "Id",
//     "Name",
//     "CreatedDate"
//   ]
// }