要在ASP.NET Core Web API中筛选GET方法，可以使用中间件或属性路由器来实现。下面是两个示例代码：

使用中间件：

public class FilterMiddleware
{
    private readonly RequestDelegate _next;

    public FilterMiddleware(RequestDelegate next)
    {
        _next = next;
    }

    public async Task Invoke(HttpContext context)
    {
        if (context.Request.Method == HttpMethod.Get.Method)
        {
            // perform filtering here
            context.Response.StatusCode = StatusCodes.Status200OK;
            await context.Response.WriteAsync("GET method is filtered");
        }
        else
        {
            await _next(context);
        }
    }
}

public class Startup
{
    public void Configure(IApplicationBuilder app, IHostingEnvironment env)
    {
        app.UseMiddleware();
    }
}

使用属性路由器：

public class ValuesController : ControllerBase
{
    private List _values = new List() { "value1", "value2", "value3" };

    [HttpGet("values")]
    public ActionResult> Get(string filter)
    {
        if (!string.IsNullOrEmpty(filter))
        {
            return _values.Where(v => v.Contains(filter)).ToList();
        }
        else
        {
            return _values.ToList();
        }
    }
}

public class Startup
{
    public void ConfigureServices(IServiceCollection services)
    {
        services.AddControllers();
    }

    public void Configure(IApplicationBuilder app)
    {
        app.UseRouting();
        app.UseEndpoints(endpoints =>
        {
            endpoints.MapControllers();
        });
    }
}

以上两个示例代码都可以实现GET方法的筛选，开发人员可以根据具体的需求来选择使用哪种方式。