Have a look at float package with its macro \newfloat to create a custom float. Alternatively, you could try toclotf but the latter is more complex. In both cases, you might also consider cleveref, which helps to customise references to your new and existing counters.
Here's one possible solution:

PS. I am not sure if Schema/Schemata is what you are up to as well as which of the form of Schemas/Schemata is correct but I think you should take on from here.
\documentclass{article}
\usepackage{graphicx}
\usepackage{float}
\newfloat{schema}{tbh}{sch}
\floatname{schema}{Schema}
\floatplacement{figure}{tbh}
\begin{document}
\listoffigures
\listof{schema}{List of Schemata}
\clearpage
Figure \ref{fig:label1}
\begin{figure}
\centering
\includegraphics[width=3cm]{example-image-a}
\caption[Short figure caption]{Very long long caption under the figure}
\label{fig:label1}
\end{figure}
Schema \ref{sch:label1}
\begin{schema}
\centering
\rule{3cm}{1.2cm}
\caption[Short schema caption]{Very very long caption under the schema}
\label{sch:label1}
\end{schema}
Figure \ref{fig:label2}
\begin{figure}
\centering
\includegraphics[width=3cm]{example-image-a}
\caption[Short figure caption]{Very long long caption under the figure}
\label{fig:label2}
\end{figure}
Schema \ref{sch:label2}
\begin{schema}[!tbh]
\centering
\rule{3cm}{1.2cm}
\caption[Short schema caption]{Very very long caption under the schema}
\label{sch:label2}
\end{schema}
\end{document}