在附加处理程序时调用这些函数，因此在没有附加适当的处理程序的情况下调用它们，而且只调用一次。
你只需要函数定义：

$('#new-quote').click(renderQuoteToPage);
...
$(document).ready(renderQuoteOnPageLoad);

• • 编辑：**每次调用getQuote()时，还需要设置randomNumber

// https://type.fit/api/quotes //
// api link for quotes //
const button = document.getElementById('new-quote');
const baseUrl = 'https://type.fit/api/quotes';
let randomNumber

function getQuote() {
  randomNumber = Math.floor(Math.random() * 100);
  fetch(baseUrl)
    .then(response => response.json())
    .then(quote => $('#text-output').text(quote[randomNumber].text))
};

function getAuthor() {
  fetch(baseUrl)
    .then(response => response.json())
    .then(quote => $('#author').text(quote[randomNumber].author))
};

function renderQuoteToPage() {
  getQuote();
  getAuthor();
}


$('#new-quote').click(renderQuoteToPage);
$(document).ready(renderQuoteToPage);

body {
  width: 100%;
  height: auto;
}

#outer-wrapper {
  display: flex;
  flex-direction: row;
  justify-content: center;
  align-items: center;
}

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<div id="outer-wrapper" class="container-fluid">

  <div id="quote-box" class="card w-50">
    <div class="card-body">

      <div class="row">
        <div class="col">
          <div id="text">
            <p id="text-output"></p>
          </div>
        </div>
      </div>

      <div class="row">
        <div class="col">
          <a href="#" id="tweet-quote">Tweet</a>
        </div>
        <div class="col">
          <div id="author">Author</div>
        </div>
      </div>

      <div class="row">
        <div class="col">
          <button id="new-quote">New quote</button>
        </div>
      </div>

    </div>
  </div>

</div>

在你的脚本和它的一些变化。

<script>
const button = document.getElementById('new-quote');
const baseUrl = 'https://type.fit/api/quotes';
let randomNumber;

function getQuote() {
  fetch(baseUrl)
  .then(response => response.json())
  .then(quote => $('#text-output').text(quote[randomNumber].text))
   };

function getAuthor() {
  fetch(baseUrl)
  .then(response => response.json())
  .then(quote => $('#author').text(quote[randomNumber].author))
};

function renderQuoteOnPageLoad() {
  randomNumber = Math.floor(Math.random() * 100);
  getQuote();
  getAuthor();
}

$(document).ready(function(){
    renderQuoteOnPageLoad();
});

 $(document).on("click","#new-quote",function(){
    renderQuoteOnPageLoad()
 })
</script>

Example Fiddle