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enter image description here

I intend to insert two figures with different sizes aligned as shown, and they should be inserted in figure* environment. Any insight will be appreciated regards shah

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I'd like to suggest that you use side-by-side subfigure environments.

In case you don't want subfigures but just "regular" figures side-by-side, I suggest you change the four instances of {subfigure} in the code shown below to {minipage} and omit the \caption{Overall figure caption} directive.

enter image description here

\documentclass[twocolumn]{article} % choose a suitable document class
\usepackage[demo]{graphicx} % remove 'demo' option in real doc.
\usepackage{subcaption} % for 'subfigure' env.
\begin{document}

\begin{figure*}
\begin{subfigure}{0.5\textwidth}
\centering
\includegraphics[width=0.8\textwidth,height=0.8\textwidth]{figa}
\caption{Caption A}
\end{subfigure}%
\begin{subfigure}{0.5\textwidth}
\centering
\includegraphics[width=0.5\textwidth,height=0.5\textwidth]{figb}
\caption{Caption B}
\end{subfigure}
\caption{Overall figure caption} % optional
\end{figure*}
\end{document}

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