首先，您似乎在jQuery选择器和其他地方使用了反号而不是撇号。这不是标准的，虽然它可能会起作用，但我建议您不要使用它，即使只是出于惯例的原因。我在这里进行了转换。
然后，我们将使用Bootstrap的模态show事件，从事件上的relatedTarget获取ID，而不是添加click处理程序。
最后，我们将使用find()方法从数组中获取相应的数据对象。
额外提示：在页面加载时获取数据一次，而不是每次单击按钮时。也就是说，如果您不希望数据频繁更改的话。

let myJson;

$('#modelId').on('show.bs.modal', function(event) {
  const id_popup = event.relatedTarget.getAttribute('data-id');

  // $.getJSON('content/js/monthjson.json', function(months) {
    const month = myJson.months.find(el => el.id == id_popup);

    $('.modal-title').text(month.georgiamonth);
    $('.modal-body').html(month.description);
  // });
});

myJson = {
  "months": [{
      "id": 1,
      "georgiamonth": "Jan",
      "description": "description Jan month",
      "suggestmonths": ""
    },
    {
      "id": 2,
      "georgiamonth": "Feb",
      "description": "description Feb month",
      "suggestmonths": ""
    },
    {
      "id": 3,
      "georgiamonth": "Mar",
      "description": "description mar month",
      "suggestmonths": ""
    },
    {
      "id": 4,
      "georgiamonth": "April",
      "description": "",
      "suggestmonths": "description April month"
    },
    {
      "id": 5,
      "georgiamonth": "May",
      "description": "description May month",
      "suggestmonths": ""
    },
    {
      "id": 6,
      "georgiamonth": "June",
      "description": "description June month",
      "suggestmonths": ""
    },
    {
      "id": 7,
      "georgiamonth": "July",
      "description": "description July month",
      "suggestmonths": ""
    },
    {
      "id": 8,
      "georgiamonth": "Aug",
      "description": "description Aug month",
      "suggestmonths": ""
    },
    {
      "id": 9,
      "georgiamonth": "Sept",
      "description": "description Sept month",
      "suggestmonths": ""
    },
    {
      "id": 10,
      "georgiamonth": "Oct",
      "description": "description Oct month",
      "suggestmonths": ""
    },
    {
      "id": 11,
      "georgiamonth": "Nov",
      "description": "description Nov month",
      "suggestmonths": ""
    },
    {
      "id": 12,
      "georgiamonth": "Dec",
      "description": "description Dec month",
      "suggestmonths": ""
    }
  ]
};

<link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/bootstrap/4.3.1/css/bootstrap.min.css" integrity="sha384-ggOyR0iXCbMQv3Xipma34MD+dH/1fQ784/j6cY/iJTQUOhcWr7x9JvoRxT2MZw1T" crossorigin="anonymous">

<button type="button" class="get-month-data btn btn-outline-danger btn-sm btn-block get-month-id" data-toggle="modal" data-target="#modelId" data-id="1">Show id 1</button>
<button type="button" class="get-month-data btn btn-outline-info btn-sm btn-block" data-toggle="modal" data-target="#modelId" data-id="2">Show id 2</button>
<button type="button" class="get-month-data btn btn-outline-warning btn-sm btn-block" data-toggle="modal" data-target="#modelId" data-id="3">Show id 3</button>
<button type="button" class="get-month-data btn btn-outline-success btn-sm btn-block" data-toggle="modal" data-target="#modelId" data-id="4">Show id 4</button>
<button type="button" class="get-month-data btn btn-outline-danger btn-sm btn-block" data-toggle="modal" data-target="#modelId" data-id="5">Show id 5</button>
<button type="button" class="get-month-data btn btn-outline-info btn-sm btn-block" data-toggle="modal" data-target="#modelId" data-id="6">Show id 6</button>
<button type="button" class="get-month-data btn btn-outline-warning btn-sm btn-block" data-toggle="modal" data-target="#modelId" data-id="7">Show id 7</button>
<button type="button" class="get-month-data btn btn-outline-success btn-sm btn-block" data-toggle="modal" data-target="#modelId" data-id="8">Show id 8</button>
<button type="button" class="get-month-data btn btn-outline-danger btn-sm btn-block" data-toggle="modal" data-target="#modelId" data-id="9">Show id 9</button>
<button type="button" class="get-month-data btn btn-outline-info btn-sm btn-block" data-toggle="modal" data-target="#modelId" data-id="10">Show id 10</button>
<button type="button" class="get-month-data btn btn-outline-warning btn-sm btn-block" data-toggle="modal" data-target="#modelId" data-id="11">Show id 11</button>
<button type="button" id="btn" class="get-month-data btn btn-outline-success btn-sm btn-block" data-toggle="modal" data-id="12" data-target="#modelId">Show id 12</button>

<div class="modal fade" id="modelId" tabindex="-1" role="dialog" aria-labelledby="modelTitleId" aria-hidden="true">
  <div class="modal-dialog" role="document">
    <div class="modal-content">
      <div class="modal-header">
        <h5 class="modal-title"> month title here </h5>
        
        <button type="button" class="close" data-dismiss="modal" aria-label="Close">
            <span aria-hidden="true">&times;</span>
        </button>
      </div>

      <div class="modal-body">
        description here
      </div>

      <div class="modal-footer">
        <button type="button" class="btn btn-secondary" data-dismiss="modal">Close</button>
      </div>
    </div>
  </div>
</div>

<script src="https://code.jquery.com/jquery-3.6.3.js" integrity="sha256-nQLuAZGRRcILA+6dMBOvcRh5Pe310sBpanc6+QBmyVM=" crossorigin="anonymous"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/popper.js/1.14.7/umd/popper.min.js" integrity="sha384-UO2eT0CpHqdSJQ6hJty5KVphtPhzWj9WO1clHTMGa3JDZwrnQq4sF86dIHNDz0W1" crossorigin="anonymous"></script>
<script src="https://stackpath.bootstrapcdn.com/bootstrap/4.3.1/js/bootstrap.min.js" integrity="sha384-JjSmVgyd0p3pXB1rRibZUAYoIIy6OrQ6VrjIEaFf/nJGzIxFDsf4x0xIM+B07jRM" crossorigin="anonymous"></script>