how can i apply sorting in string in mongodb

this is my sample document

{
  "string" : "class.chapter.1.topic.10"
}

how can I sort this string according to "chapter.anynumber.topic.anynumber"

Not exactly scientific, but here is one way:

db.collection.aggregate([
  {
    "$project": {
      string: "$string",
      chapter_num: {
        "$toInt": {
          $arrayElemAt: [
            {
              $split: [
                "$string",
                "."
              ]
            },
            2
          ]
        }
      },
      topic_num: {
        "$toInt": {
          $arrayElemAt: [
            {
              $split: [
                "$string",
                "."
              ]
            },
            4
          ]
        }
      }
    }
  },
  {
    $sort: {
      chapter_num: 1,
      topic_num: 1
    }
  },
  {
    "$project": {
      string: "$string"
    }
  }
])

What it does is split the string by ., then grab elements 2 and 4 as chapter_num and topic_num of the resulting array, convert them to Int and sort it with:

  {
    $sort: {
      chapter_num: 1,
      topic_num: 1
    }
  }

toggle between 1 and -1 to go asc or desc.

Note that this assumes that your string will adhere to this format: xxx.xxx.num.xxx.num.

If used against this sample collection:

[
  {
    "string": "class.chapter.1.topic.10"
  },
  {
    "string": "class.chapter.2.topic.3"
  },
  {
    "string": "class.chapter.1.topic.12"
  },
  {
    "string": "class.chapter.1.topic.1"
  }
]

The result will be:

[
  {
    "_id": ObjectId("5a934e000102030405000003"),
    "string": "class.chapter.1.topic.1"
  },
  {
    "_id": ObjectId("5a934e000102030405000000"),
    "string": "class.chapter.1.topic.10"
  },
  {
    "_id": ObjectId("5a934e000102030405000002"),
    "string": "class.chapter.1.topic.12"
  },
  {
    "_id": ObjectId("5a934e000102030405000001"),
    "string": "class.chapter.2.topic.3"
  }
]

Playground: https://mongoplayground.net/p/6-2QRIppu0u