I use Vim a lot for writing tasks and I used ^p for completions. However, is there a plugin that suggests you completions while typing like in Andriod-smartphones ? Thanks.
By "suggests you completions" I assume you mean that the completion popup appears automatically without interrupting your typing. If so, yes, there are a number of them. To name two AutoComplPop and YouCompleteMe.
You can use VimAwesome to search for others. It has an entire category dedicated to "autocomplete", a super set of the type of plugin you're interested in. Included are the two mentioned by Karl in the comments below: nvim-completion-manager and deoplete.