Document: caretPositionFromPoint() メソッド

caretPositionFromPoint(x, y)

function insertBreakAtPoint(e) {
  let range;
  let textNode;
  let offset;
  if (document.caretPositionFromPoint) {
    range = document.caretPositionFromPoint(e.clientX, e.clientY);
    textNode = range.offsetNode;
    offset = range.offset;
  } else if (document.caretRangeFromPoint) {
    // WebKit 独自の代替メソッドを使用
    range = document.caretRangeFromPoint(e.clientX, e.clientY);
    textNode = range.startContainer;
    offset = range.startOffset;
  } else {
    // どちらのメソッドも対応していなければ、何もしない
    return;
  }
  // TEXT_NODE のみを分割
  if (textNode?.nodeType === 3) {
    let replacement = textNode.splitText(offset);
    let br = document.createElement("br");
    textNode.parentNode.insertBefore(br, replacement);
  }
}
let paragraphs = document.getElementsByTagName("p");
for (const paragraph of paragraphs) {
  paragraph.addEventListener("click", insertBreakAtPoint, false);
}

let message = document.getElementById("message");
if (document.caretPositionFromPoint) {
  message.textContent =
    "このブラウザーは標準の document.caretPositionFromPoint に対応しています";
  message.classList.add("supported");
} else if (document.caretRangeFromPoint) {
  message.textContent =
    "このブラウザーは標準外の document.caretRangeFromPoint に対応しています";
  message.classList.add("supported");
}

<div id="message">
  このブラウザーは document.caretRangeFromPoint にも
  document.caretPositionFromPoint にも対応していません。
</div>

<p>
  Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy
  eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam
  voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita
  kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.
</p>

#message {
  color: red;
  font-weight: bold;
}
#message.fallback {
  color: darkorange;
}
#message.supported {
  color: green;
}