How to add a new Object to a property of object in a model

As I understand, you want to embed courses into the user model.

So you need to make this change in your user model:

const mongoose = require("mongoose");
const Schema = mongoose.Schema;

let userSchema = new Schema({
  email: { type: String, required: true },
  password: { type: String, required: true },
  name: { type: String, required: true },
  phoneNumber: { type: Number, required: true },
  schedule: { type: String, required: true },
  courses: [
    new Schema({
      name: String
    })
  ]
});

module.exports = mongoose.model("User", userSchema);

And create a course for the given user like this:

app.post("/user/:id/course", async (req, res) => {
  const result = await User.findByIdAndUpdate(
    req.params.id,
    {
      $push: {
        courses: {
          name: req.body.name
        }
      }
    },
    {
      new: true
    }
  );

  res.send(result);
});

When you send a request to url http://localhost:3000/user/5de2cf9323f76c207c233729/course with this body: (Note that 5de2cf9323f76c207c233729 is an existing user _id)

{
  "name": "Course 1"
}

The response will be like this, meaning the course is added to the user:

{
    "_id": "5de2cf9323f76c207c233729",
    "email": "[email protected]",
    "password": "123123",
    "name": "Max",
    "phoneNumber": 123123123,
    "schedule": "sc1",
    "courses": [
        {
            "_id": "5de2cfa723f76c207c23372a",
            "name": "Course 1"
        }
    ],
    "__v": 0
}