Go to Telegram Settings, scroll down and long tap 2 times on version number, then choose "Reset chats" option. No data will be lost or deleted.
When reading old chats some parts of the chat history are not loaded. As you can see in video when I scroll down my chat from October 2, 2018 it suddenly goes to July 21.
Ps: We have chat history in 3, 4 October (and day and month after it) but as you can see it will skips those chats.
Note: The missing parts of the history are visible from Telegram Desktop
Steps to reproduce
As I just seen this behavior in one of my chats (not sure this behavior occurs in my other chats or not) I reproduce steps specially for this chat:
Open a chat
In a chat, tap the three dot button and click on Search
Search a text related to old chat history
Scroll down from that searched result and you can see it jump over dates and skips some messages.
Current result
Parts of the chat history are skipped
Expected result
All the chat history is visible
Device info
Telegram Android 8.0.0 (24069), Xiaomi Mi 9T, 11 R? (30)
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Please go to settings, scroll down and long tap 2 times on version number. Choose "Reset chats" option.
Let us know if this fixed your issue.