Modified Preamble

\documentclass[12pt,oneside,letter]{article}

% Modified Preamble
\usepackage{amssymb}
\usepackage{graphicx,rotating}
\usepackage{amscd}
\usepackage{color}
\usepackage{newtxtext}
\usepackage{float}
%\usepackage{psfig}
\usepackage{graphics}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{mathrsfs}
\usepackage{amsthm}
\usepackage{amsfonts}
\usepackage{latexsym}
\usepackage{epsf}
\usepackage[center]{titlesec}
\usepackage[]{hyperref}
\usepackage{mathptmx}
\usepackage{longtable}
\usepackage{array}
\usepackage{csquotes}
\usepackage{verbatim}
\usepackage{enumerate}
\usepackage[left=1.5in, top=1in, right=1in, bottom=1in]{geometry}
\usepackage{rotating}
\usepackage{caption}
\usepackage{mdframed}
\usepackage{colortbl}
\usepackage{setspace}
\usepackage{mathptmx}
\usepackage{setspace}
\usepackage[mathscr]{euscript}
\usepackage{fancyhdr}
\usepackage{sectsty}


\pagestyle{fancy}
\fancyhf{}
\fancyheadoffset{0cm}
\renewcommand{\headrulewidth}{0pt}
\renewcommand{\footrulewidth}{0pt}
\fancyhead[R]{\thepage}
\fancypagestyle{plain}{%
    \fancyhf{}%
    \fancyhead[R]{\thepage}%
}


\allsectionsfont{\centering \fontsize{12}{15}\selectfont}
\subsectionfont{\centering \fontsize{12}{15}\selectfont }
\setcounter{secnumdepth}{0}


\newcolumntype{P}[1]{>{\centering\arraybackslash}p{#1}}
\newmdtheoremenv{theo}{Theorem}
\def\nams{\\ \noalign{\medskip}}
\def\mybibitem{%
    \vskip\baselineskip% % space above
    \noindent%           % suppress regular indent
    \hangindent=1.5em%   % indent same amount as `quotation` environment
}

% -------------------------------------------------------------------------------------------------
\renewcommand{\baselinestretch}{1}
\renewcommand{\contentsname}{CONTENTS}
\pagestyle{myheadings}
\thispagestyle{empty}
\date{}

%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
% Define a new theorem style with normal font
\newtheoremstyle{mystyle}% name
{\topsep}%      Space above
{\topsep}%      Space below
{\normalfont}%  Body font
{}%             Indent amount
{\bfseries}%    Theorem head font
{.}%            Punctuation after theorem head
{.5em}%         Space after theorem head
{}%             Theorem head spec (can be left empty, meaning 'normal')

% Use the new theorem style for all theorem-like environments
\theoremstyle{mystyle}
\newtheorem{result}{Theorem}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{corollary}{Corollary}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{remark}{Remark}
\newtheorem{illustration}{Illustration}
\date{}

\doublespacing
\begin{document}
\end{document}