The MWE is as follows:
\documentclass[12pt,letter]{report}
\usepackage[titles]{tocloft}
\usepackage[compact,tiny]{titlesec}
\begin{document}
\setcounter{tocdepth}{3}
\setlength\cftaftertoctitleskip{0pt}
\titlespacing*{\chapter}{0.00in}{0.48in}{5mm}
\titleformat{\chapter}[display]{\normalfont\normalsize\filcenter}{%
\centering\chaptertitlename\ \thechapter}{0pt}{\normalsize\uppercase}
\renewcommand{\contentsname}{TABLE OF CONTENTS}
\renewcommand{\cftchapfont}{\normalsize}
\renewcommand{\cftchappagefont}{\normalsize}
\renewcommand{\cftchapleader}{\normalsize\cftdotfill{\cftchapdotsep}}
\tableofcontents
\univchapter[first chapter]{first chapter}
some text
\univchapter[second chapter]{second chapter}
some more text
\end{document}
The definition of \univchapter is
\newcommand\univchapter{\if@openright\cleardoublepage\else\clearpage\fi
\thispagestyle{plain}%
\global\@topnum\z@
\@afterindentfalse
\secdef\@univchapter\@schapter}
\def\@univchapter[#1]#2{\ifnum \c@secnumdepth >\m@ne
\refstepcounter{chapter}%
\typeout{\@chapapp\space\thechapter.}%
\addcontentsline{toc}{chapter}%
{\chaptername\, \protect\numberline{\thechapter} \uppercase{#1}}%
\else
\addcontentsline{toc}{chapter}{\chaptername\, \uppercase{#1}}%
\fi
\chaptermark{#1}%
\addtocontents{lof}{\protect\addvspace{10\p@}}%
\addtocontents{lot}{\protect\addvspace{10\p@}}%
\if@twocolumn
\@topnewpage[\@makechapterhead{#2}]%
\else
\@makechapterhead{#2}%
\@afterheading
\fi}
The error it generates while creating a MWE and also while executing the code with your suggestion is Use of \@ doesnt match its definition. \univchapter...i\thispagestyle{plain}global \@t opnum\z@afterindentfal....

