Q:

Why Subsection at top-bar in fancyhdr? 

Code 
\documentclass{article}

\usepackage{fancyhdr}

\pagestyle{fancy}
\rhead{\textsc{Department}}
\cfoot{\thepage}

\begin{document}

% \section{Objective Data} % nothing at left top when this active

\subsection{Status localis}

Hello world

\end{document}

Output

Expected output: without 0.1 Status localis at the top-left bar.  

How can you have no subsection at top-left bar?  

A:

Just say \lhead{}, i.e. an empty left page heading, because this is used by \leftmark{} normally, which prints a section etc.  title.  
\documentclass{article}

\usepackage{fancyhdr}

\pagestyle{fancy}
\rhead{\textsc{Department}}
\lhead{}%
\cfoot{\thepage}

\begin{document}

%\section{Objective Data} % nothing at left top when this active

\subsection{Status localis}

Hello world

\end{document}

