var requestURL = "api/EmployeeApi/GetEmployeeByName";
var dataJSON = {};
dataJSON["name"] = "Albert";

$.ajax({
    url: requestURL,
    data: JSON.stringify(dataJSON),
    type: "POST",
    dataType: "json",
    contentType: "application/json;charset=utf-8",
    success: function(returnData){
        console.log(returnData);
    },
    error: function(xhr, ajaxOptions, thrownError){
        console.log(xhr.status);
        console.log(thrownError);
    }
});

#button_search

你確定Get的data不是寫在網址後面的嗎?

1.我覺得你先用postman測試你的後端要輸入怎樣的url 才可以回傳訊息
把postman成功get樣子放上來可以更好幫助你找問題
版上postman文章:https://ithelp.ithome.com.tw/articles/10201503
2.我猜你要get的url可能長api/EmployeeApi/GetEmployeeByName?name=Albert