Tumtum and androginos are two sexes which are distinct from male and female in halacha. While in practice, they are rarer today due to advances in medical technology, it would still be possible for them to exist.
Assuming this, where would a tumtum or an androginos sit in schul?
It would appear that he sits in the men's section since he looks like a man.
He needs to dress like a man, have Payos-sideburns (and a beard/shave) like a man and put on Tallis and Tefillin like a man.
Source: 4th chapter of ביכורים (which is really a תּוֹסֶפְתָּא), Mishna 2:
ב: כֵּיצַד שָׁוֶה לָאֲנָשִׁים. מְטַמֵּא בְלֹבֶן, כָּאֲנָשִׁים. וְנוֹשֵׂא, אֲבָל לֹא נִשָּׂא, כָּאֲנָשִׁים. וְאִמּוֹ יוֹשֶׁבֶת עָלָיו בְּדַם טֹהַר, כָּאֲנָשִׁים. וְאֵינוֹ מִתְיַחֵד עִם הַנָּשִׁים, כָּאֲנָשִׁים. וְאֵינוֹ נִזּוֹן עִם הַבָּנוֹת, כָּאֲנָשִׁים. וּמִתְעַטֵּף, כָּאֲנָשִׁים. וְעוֹבֵר עַל בַּל תַּקִּיף וְעַל בַּל תַּשְׁחִית וְעַל בַּל תִּטָּמֵּא לְמֵתִים, כָּאֲנָשִׁים. וְחַיָּב בְּכָל הַמִּצְוֹת הָאֲמוּרוֹת בַּתּוֹרָה, כָּאֲנָשִׁים:
How are they he similar to men? They become impure from seminal discharges like men, they can marry (a woman) but can't be married (to a man) like men, their mother only gets 7 clean days as if she gave birth to a boy, they cannot be secluded with women, like men, they don't get fed with the daughters (as orphans if there are limited funds) like sons, they get dressed like men, they transgress shaving off sideburns and beards-with-a-blade like men, they may not become impure to corpses (if they are Cohanim) like men, and they are obligated to keep all Mitzvoth in the Torah, like men.
ר"ע מברטנורה
וּמִתְעַטֵּף כָּאֲנָשִׁים. שֶׁלֹּא יִלְבַּשׁ שִׂמְלַת אִשָּׁה:
וְחַיָּב בְּכָל הַמִּצְוֹת כָּאֲנָשִׁים. אֲפִלּוּ מִצְוַת עֲשֵׂה שֶׁהַזְּמַן גְּרָמָא שֶׁהַנָּשִׁים פְּטוּרוֹת, הוּא חַיָּב:Bartenura:
Get dressed like men: i.e. they may not wear dresses like women.
They are obligated to keep all Mitzvoth in the Torah, like men: even time bound Mitzvoth from which women are exempted, they are obligated to keep.
That's besides for the potential Yichud issue, and we pasken that they may seclude themselves with men but not with women.
שלחן ערוך - אבן העזר-סימן כב - אסור יחוד, ועם מי אסור להתיחד
י"ב: אַנְדְּרוֹגֵינוֹס, אֵינוֹ מִתְיַחֵד עִם הַנָּשִׁים. וְאִם נִתְיַחֵד, אֵין מַכִּין אוֹתוֹ, מִפְּנֵי שֶׁהוּא סָפֵק. אֲבָל הָאִישׁ מִתְיַחֵד עִם הָאַנְדְּרוֹגֵינוֹס וְעִם הַטֻּמְטוּם:Shulchan Aruch - Even HaEzer 22
12: An Androginus may not seclude himself with women, and if they transgressed the laws of Yichud they do not get whipped (by Bet Din), since they are possibly not really male. However, a man may seclude himself with a Tumtum or Androginus.
