You basically need telegram api then? are you asking about general approach or specific issue here?

General approach

I've read the telegram docs and didn't found what I looking for

add you bot to your channel (as normal user) and then use the endpoint to read the chat history. The correct endpoint should be: https://core.telegram.org/method/messages.getHistory

import { NextResponse } from 'next/server';

const TELEGRAM_BOT_TOKEN = process.env.TELEGRAM_BOT_TOKEN;
const TELEGRAM_CHANNEL_USERNAME = process.env.TELEGRAM_CHANNEL_USERNAME;

export async function GET() {
  try {
    const response = await fetch(
      `https://api.telegram.org/bot${TELEGRAM_BOT_TOKEN}/getUpdates?chat_id=@${TELEGRAM_CHANNEL_USERNAME}&limit=10`
    );
    const data = await response.json();

    if (!data.ok) {
      throw new Error('Failed to fetch Telegram posts');
    }

    const posts = data.result
      .filter((update: any) => update.channel_post)
      .map((update: any) => update.channel_post);

    return NextResponse.json({ posts });
  } catch (error) {
    console.error('Error fetching Telegram posts:', error);
    return NextResponse.json({ error: 'Failed to fetch Telegram posts' }, { status: 500 });
  }
}

This can be used as API route that fetches latest updates from telegram api

then in your page, call this api in interval - not sure what did you mean by "real time" but this approach should work mostly

It's a public channel.
Not a chat.
Will this work

I haven't tried it yet. Try and see