Based on my answer at What are the ways to position things absolutely on the page?.
EDITED to handle x alignment with different font sizes.
This approach can be combined in a macro with alignments in the form of
\aligntext[<font-size>]{<x>}{<y>}{<l/c/r>}{<t/b/B/x>}{<content>}
where <l/c/r> is for left/center/right alignment and <t/b/B/x> is for top/bottom/BASELINE/ex alignment, relative to the specified (x,y) coordinate. By "ex" alignment, I mean alignment to a vertical location 1ex above the baseline. These four vertical alignments correspond to the red dot locations of the OP's figure.
To show it best, I also provide an \aligntextref macro with the same argument stream that places a red dot centered at the given (x,y) location, so that the alignment can be checked.
The EDIT was necessary because when changing fontsize in the content of the argument, the size of the 1ex shift (for x alignment) did not revise itself to the new font size until too late. As shown in the updated MWE, the <fontsize> in the optional argument can be given as \Huge, \tiny, etc. However, it can also be given as \fontsize{16pt}{16pt}\selectfont, for example.
Here is the MWE.
\documentclass{article}
\usepackage{everypage,xcolor}
\usepackage{stackengine}
% THESE ARE LaTeX DEFAULTS; CAN CHANGE IF NEEDED.
\def\PageTopMargin{1in}
\def\PageLeftMargin{1in}
\newcommand\atxy[3]{%
\AddThispageHook{\smash{\hspace*{\dimexpr-\PageLeftMargin-\hoffset+#1\relax}%
\raisebox{\dimexpr\PageTopMargin+\voffset-#2\relax}{#3}}}}
\newcommand\aligntext[6][\normalsize]{%
\if B#5\atxy{#2}{#3}{#1\makebox[0pt][#4]{#6}}\else%
\if x#5\atxy{#2}{#3}{#1\raisebox{-1ex}{\makebox[0pt][#4]{#6}}}\else%
\if b#5\atxy{#2}{#3}{#1\abovebaseline[0pt]{\makebox[0pt][#4]{#6}}}\else%
\if t#5\atxy{#2}{#3}{#1\belowbaseline[0pt]{\makebox[0pt][#4]{#6}}}\fi\fi\fi\fi%
}
\newcommand\aligntextref[6][\normalsize]{%
\aligntext[#1]{#2}{#3}{#4}{#5}{#6}%
\aligntext[#1]{#2}{#3}{c}{B}{\color{red}\makebox[0pt]{\rule[-.4pt]{.8pt}{.8pt}}}%
}
\begin{document}
\aligntext{0\paperwidth}{0\paperheight}{l}{t}{Top left alignment}
\aligntext{.5\paperwidth}{0\paperheight}{c}{x}{Top x alignment}
\aligntext{1\paperwidth}{0\paperheight}{r}{t}{Top right alignment}
\aligntext{0\paperwidth}{1\paperheight}{l}{b}{Bottom left alignment}
\aligntext{.5\paperwidth}{1\paperheight}{c}{B}{BASELINE center alignment}
\aligntext{1\paperwidth}{1\paperheight}{r}{b}{Bottom right alignment}
\mbox{}
\aligntextref{100pt}{100pt}{r}{t}{X}
\aligntextref{120pt}{100pt}{l}{t}{fg}
\aligntextref{110pt}{100pt}{c}{t}{x}
\aligntextref{100pt}{115pt}{r}{x}{X}
\aligntextref{120pt}{115pt}{l}{x}{fg}
\aligntextref{110pt}{115pt}{c}{x}{x}
\aligntextref{100pt}{130pt}{r}{B}{X}
\aligntextref{120pt}{130pt}{l}{B}{fg}
\aligntextref{110pt}{130pt}{c}{B}{x}
\aligntextref{100pt}{145pt}{r}{b}{X}
\aligntextref{120pt}{145pt}{l}{b}{fg}
\aligntextref{110pt}{145pt}{c}{b}{x}
\aligntextref[\Huge]{110pt}{185pt}{l}{x}{x alignment Huge}
\aligntextref[\tiny]{110pt}{185pt}{r}{x}{x alignment tiny}
\aligntext{140pt}{100pt}{l}{t}{Top alignment}
\aligntext{140pt}{115pt}{l}{x}{Ex alignment}
\aligntext{140pt}{130pt}{l}{B}{Baseline alignment}
\aligntext{140pt}{145pt}{l}{b}{bottom alignment}
\end{document}

The EDIT provides the fix for the next image.







Note: A page composed completely of \aligntext calls will produce no output unless something is added as normal text to the page. That is why the MWE has a \mbox{} mixed in, so as to trigger the normal page production.