How can I make a 45 degree responsive ribbon with folded corner?

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You can try like below:

.container {
  width: 200px;
  height: 150px;
  position: relative;
  display:inline-block;
  margin: 10px;
  background: lightblue;
}

.stack-top {
  /* adjust the below to control the shape */
  --d:5px; 
  --g:16px;
  --c:#333;
  /**/

  position: absolute;
  top: 0;
  right: 0;
  transform: translate(29.29%, -100%) rotate(45deg); /* 29.29% = 100%*(1 - cos(45deg)) */
  color: #fff;
  text-align: center;
  width: 100px;
  transform-origin: bottom left;
  padding:5px 0 calc(var(--d) + 5px);
  background:
    linear-gradient(135deg, transparent var(--g), var(--c) calc(var(--g) - 0.3px)) left,
    linear-gradient(-135deg,transparent var(--g), var(--c) calc(var(--g) - 0.3px)) right;
  background-size:51% 100%;
  background-repeat:no-repeat;
  clip-path:polygon(0 0,100% 0,100% 100%, calc(100% - var(--d)) calc(100% - var(--d)), var(--d) calc(100% - var(--d)),0 100%)
}
<div class="container">
  <div class="stack-top">1Month</div>
</div>

<div class="container">
  <div class="stack-top" style="--d:0px;--g:19px;width:120px;--c:blue">1Month</div>
</div>

<div class="container">
  <div class="stack-top" style="--d:8px;--g:17px;width:80px;--c:red">XX</div>
</div>

<div class="container">
  <div class="stack-top" style="--d:10px;--g:20px;width:200px;--c:green">1Month</div>
</div>

CSS responsive folded ribbon

Another adjustment to add a shadow effect to the folded part:

.container {
  width: 200px;
  height: 150px;
  position: relative;
  display:inline-block;
  margin: 10px;
  background: lightblue;
}

.stack-top {
  /* adjust the below to control the shape */
  --d:5px; 
  --w:100px;
  --c:#333;
  /**/

  position: absolute;
  top: 0;
  right: 0;
  transform: translate(29.29%, -100%) rotate(45deg); /* 29.29% = 100%*(1 - cos(45deg)) */
  color: #fff;
  text-align: center;
  width: var(--w);
  transform-origin: bottom left;
  padding:5px 0 calc(var(--d) + 5px);
  background:
    linear-gradient(rgba(0,0,0,0.6) 0 0) bottom/100% var(--d) no-repeat
    var(--c);
  clip-path:polygon(0 100%,0 calc(100% - var(--d)),50% calc(100% - var(--d) - var(--w)/2),100% calc(100% - var(--d)),100% 100%,calc(100% - var(--d)) calc(100% - var(--d)), var(--d) calc(100% - var(--d)))
}
<div class="container">
  <div class="stack-top">1Month</div>
</div>

<div class="container">
  <div class="stack-top" style="--d:0px;--w:120px;--c:pink">1Month</div>
</div>

<div class="container">
  <div class="stack-top" style="--d:8px;--w:80px;--c:red">XX</div>
</div>

<div class="container">
  <div class="stack-top" style="--d:12px;--w:200px;--c:green">1Month</div>
</div>

CSS diagonal ribbon corner

You can add position option:

.container {
  width: 200px;
  height: 150px;
  position: relative;
  display:inline-block;
  margin: 10px;
  background: lightblue;
}

.stack-top {
  /* adjust the below to control the shape */
  --d:5px; 
  --w:100px;
  --c:#333;
  /**/

  position: absolute;
  top: 0;
  right: 0;
  transform: translate(29.29%, -100%) rotate(45deg); /* 29.29% = 100%*(1 - cos(45deg)) */
  color: #fff;
  text-align: center;
  width: var(--w);
  transform-origin: bottom left;
  padding:5px 0 calc(var(--d) + 5px);
  background:
    linear-gradient(rgba(0,0,0,0.6) 0 0) bottom/100% var(--d) no-repeat
    var(--c);
  clip-path:polygon(0 100%,0 calc(100% - var(--d)),50% calc(100% - var(--d) - var(--w)/2),100% calc(100% - var(--d)),100% 100%,calc(100% - var(--d)) calc(100% - var(--d)), var(--d) calc(100% - var(--d)))
}

.stack-top.left {
  left:0;
  right:auto;
  transform: translate(-29.29%, -100%) rotate(-45deg);
  transform-origin: bottom right;
}
<div class="container">
  <div class="stack-top">1Month</div>
</div>

<div class="container">
  <div class="stack-top" style="--d:0px;--w:120px;--c:pink">1Month</div>
</div>

<div class="container">
  <div class="stack-top left" style="--d:8px;--w:80px;--c:red">XX</div>
</div>

<div class="container">
  <div class="stack-top left" style="--d:12px;--w:200px;--c:green">1Month</div>
</div>

CSS folded ribbon multi-position

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