FA few weeks ago I started training again.

I picked jogging to start with because (I (think) I am good at ithis.

Whatever you put in parentheses should be completely removable without making the sentence grammatically incorrect.

Well, I didIn fact, I have completed a couples marathons in lthe past 15 years.

So, each day jogging one hour each day isn’t hard for me.

Natural to connect this to the previous sentence.

I also thinking that was a personal goal.

Not sure what you mean here. You were thinking of a personal goal? Or you wanted an hour of jogging each day to be your personal goal? Or running a marathon again is a personal goal?

After I had been jogging in the same sport hallgym for a week.,

"Sport hall" isn't a thing in English, you probably mean gym, which can either be a place with a lot of exercise equipment or a really big room to run in/play sports in, chiefly basketball.

I noticed a lot of people jogging at the same time withas me.

Connect to last sentence.

There are a few personsople who are older than me but jogginwho still jog faster than me.,

Above is what I think you meant, you might also have meant "there are few (people) older than me who jog faster than me," which is equivalent to "there are not many people who are older than me and also jog faster than me"

Aand other few personsa few others who comes to this sport halle gym more often than me.

Connect to previous sentence

Because of them I did feel a little angryI feel a little envious/jealous of them!