Либо использовать async/await
const myArray = ["1", "2", "3", "4"];
(async function (array) {
  for (item of array) {
    await fetch(`https://jsonplaceholder.typicode.com/posts/${item}`)
      .then((response) => response.json())
      .then((response) => console.log(response))
      .catch((error) => console.error(error));
  }
})(myArray);
Либо reduce
const myArray = ["1", "2", "3", "4"];
myArray.reduce((p, item) => {
  return p
    .then(() => fetch(`https://jsonplaceholder.typicode.com/posts/${item}`))
    .then((response) => response.json())
    .then((response) => console.log(response))
    .catch((error) => console.error(error));
}, Promise.resolve());