[Vuejs]-I want to show Modal box when I click a button in VUE js

You can look up page source to see if component is rendered.

Your modal is hidden by default. You can change following:

    <div class="modal fade">

To

    <div class="modal fade show">

Add component to Vue instance

const modalregister = Vue.component('modalregister',{...

new Vue({
el:'#register-wrap',
components: { modalregister },
...