[Vuejs]-Vue displaying array elements via search on button click

You should use computed property to filter out results you fetched in mounted hook. You can check out vue.js documentation example with similar functionality here – https://v2.vuejs.org/v2/guide/list.html#v-for-with-a-Component.

If you want to make separate API call for every search request, then just implement search method and use your this.creditid as parameter and replace credits array with API response data – example https://jsfiddle.net/qrwn568g/1/ (added axios for http request handling and tailwind for a little styling)