I was watching Otherworlds TV on Roku this morning and this blast from the past occurred.
The cartoons were about 3 1/2 minutes long and in color, and there were about 100 of them in total. A single story consisted of 10 episodes.
Clue #A: Syndicated cartoon.
The Adventures of Rocky and Bullwinkle?
Beyond the fact that it was a syndicated cartoon…no.
This one ran for about a year, and was in color.
Courageous Cat and Minute Mouse?
Underdog?
Grape Ape?
Speed Buggy?
Hong Kong Phooey?
A lot of possibilities based on the description.
I don’t think any of them are possibilities based on the description in the OP and the clues given afterward.
Another clew for yew: 1960-1961.
Mr. Magoo?
King Leonardo and His Short Subjects?
The cartoons were about 3 1/2 minutes long and in color, and there were about 100 of them in total. A single story consisted of 10 episodes.
It ran for a year from 1960 to 1961.
It was in color.
King Leonardo was an NBC cartoon, and didn’t consist of ten 31/2 minute segments making up each story.
Yeah, I was just trying to remember by year. Tom Terrific had episodes, but only five to a story, and I’m thinking he was earlier than 1960. I’ll keep thinking.
Courageous Cat and Mr Magoo (the TV series) come very close to all of those criteria. As much as I am a cartoon afficionado, you are clearly looking for something more obscure. I concede.
Was it shown on Garfield Goose?
Neither one of those featured 10-part continued stories, or ran for just one year, I don’t think.
Not that I know of. Mine had 10 10-part stories for a total of 100 episodes.
Mr. Magoo (the TV series) had 130 episodes and ran from 1960-61. Courageous Cat had 92 episodes and ran from 1960-62. I watched them both in syndication as a child, but have no idea if they were serialized.
Hmm, Tintin ran for too long, though the era is about right. This is tough!
I Googled it, and probably found it. I don’t remember ever seeing it or hearing about it.
Very obscure Wiki clue…unless you understand the language. “In Japan, it was dubbed into Japanese and broadcast on Fuji Television from May 15, 1962 to January 3, 1963 under the name “探偵スカット”.” 
Gonna keep it on the Q.T.?