No, jQuery and Vue.js are different libraries and can be used together. Instead you should learn JavaScript (ES5, ES6, ES7) itself, Web Standards, Web APIs, DOM, UI, accessibility. jQuery is not needed since ES5. However, it is still a solid choice when you need a fast temporary solution which exists only with jQuery.
jQuery is a DOM library which was written 10+ years ago to make cross-browser DOM manipulation easy because then there were a lot of problems in cross-browser support and many simple features were missing in JS.
Vue.js is a library for building components like a React.
Instead of learning a framework/library after learning a language you should learn software design patterns and principles. You can write complicated modern apps in Vanilla JS when you know JS and software architecture, software engineering and software design. Moreover this knowledge can be applied in every field and it won't change much during your lifetime while all those libraries go, change and die every month.
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