[Vuejs]-Vuejs Add Router Link With Js Append

You can’t append router-link to html after Vue is rendered, router-link will be rendered to a tag when Vue loads. try using v-if in your template instead of append in jquery. when you use v-if, item will not be inserted in the document unless your condition is true.
you can checkout Vue conditional rendering document:
https://vuejs.org/guide/essentials/conditional.html#v-if