documentclass{memoir}
usepackage{lipsum}

usepackage[american]{babel}
usepackage[utf8]{inputenc}
usepackage{csquotes}

makeatletter
renewcommand{@chapapp}{Segment}
makeatother

usepackage{nameref}

usepackage[T1]{fontenc}
usepackage[
    backend=biber,
    %bibencoding=utf8,
    % refsection=chapter,
    refsegment=subsection+,
    url=false,
    sorting=none,
    sortcites=true,
    sorting=nyt,
    style=apa
    %style=numeric
]{biblatex}
% DeclareLanguageMapping{american}{american-apa}

makeatletter
%newcommand*{currentname}{@currentlabelname}
makeatother


% segmented bibliography
defbibheading{subbibliography}{subsection*{References for  Segment~ref{refsegment:therefsectiontherefsegment}: nameref{refsegment:therefsectiontherefsegment} }}

% DefineBibliographyStrings{english}{%
%   references = {Works Cited},
% }

addbibresource{biblatex-examples.bib}

usepackage[]{hyperref}
hypersetup{
    colorlinks=false,
}


begin{document}

author{John Doe}
title{Bla bla}

tableofcontents

chapter{First, there was light}
% label{chapter1}

lipsum[0-1]
Cite an author not previously cited~cite{cicero}.
Note: Alphabetcially, K comes before S.

section{A Section}

lipsum[0-1]
Cite an author not previously cited~cite{cicero}.
Note: Alphabetcially, K comes before S.

chapter{Then, there was a power outage}
% label{chapter2}

lipsum[0-1]
And then again cite some authoprs cited previously~cite{kastenholz}.
At vero eos et accusam et justo duo dolores et ea rebum~cite{sigfridsson}.

printbibheading
% bibbysection[heading=subbibliography]
bibbysegment[heading=subbibliography]

end{document}

section{A Section}
newrefsegment