How to run my Vue app if have inside private registry package?

Question

I cloned a Vue app from git which I am trying to install npm install command, but this gives me the following error:

npm ERR! notarget No matching version found for [email protected].
npm ERR! notarget In most cases you or one of your dependencies are requesting
npm ERR! notarget a package version that doesn't exist.
npm ERR! notarget 
npm ERR! notarget It was specified as a dependency of 'scoring-frontend'
npm ERR! notarget 

npm ERR! A complete log of this run can be found in:
npm ERR!     /Users/obidjon/.npm/_logs/2022-07-21T05_54_41_930Z-debug.log

My package.json files is as follows:

  "name": "scoring",
  "version": "0.1.0",
  "private": true,
  "scripts": {
    "serve": "vue-cli-service serve",
    "build": "vue-cli-service build",
    "test:unit": "vue-cli-service test:unit",
    "lint": "vue-cli-service lint",
    "bekit": "npm i bekit --registry http://localhost:4888"
  },
  "dependencies": {
    "bekit": "^1.0.44",
    "core-js": "^3.6.5",
    "ky": "^0.27.0",
    "precss": "^4.0.0",
    "v-calendar": "^2.3.0",
    "vue": "^2.6.11",
    "vue-i18n": "^8.24.2",
    "vue-recaptcha": "^1.3.0",
    "vue-router": "^3.2.0",
    "vue-the-mask": "^0.11.1",
    "vuelidate": "^0.7.6",
    "vuex": "^3.4.0"
  },
  "devDependencies": {
    "@vue/cli-plugin-babel": "~4.5.0",
    "@vue/cli-plugin-eslint": "~4.5.0",
    "@vue/cli-plugin-router": "~4.5.0",
    "@vue/cli-plugin-unit-jest": "~4.5.0",
    "@vue/cli-plugin-vuex": "~4.5.0",
    "@vue/cli-service": "~4.5.0",
    "@vue/eslint-config-standard": "^5.1.2",
    "@vue/test-utils": "^1.0.3",
    "babel-eslint": "^10.1.0",
    "eslint": "^6.7.2",
    "eslint-plugin-import": "^2.20.2",
    "eslint-plugin-node": "^11.1.0",
    "eslint-plugin-promise": "^4.2.1",
    "eslint-plugin-standard": "^4.0.0",
    "eslint-plugin-vue": "^6.2.2",
    "vue-template-compiler": "^2.6.11"
  }
}

Scripts in package.json have bekit registry and it cannot be installed.

I try to install bekit from npmjs which is https://www.npmjs.com/package/bekit ( npm i bekit). But This is completely different.

How to use this private registry which is bekit ????