Cllr Michelle Donohue-Moncrief, 43, of Northgate, Hunmanby, screamed into the ear of Cllr Heather Phillips for "10 to 15 seconds" at a meeting of the Rough Sleeping Taskgroup on February 16.
At Scarborough Magistrates' Court today Cllr Donohue-Moncrief, through her solicitor, apologised for her actions and said she intends to stay on as councillor for Hertford ward.
Alison Whiteley, prosecuting, told the court that Cllr Phillips had previously tried to help her fellow councillor through some personal problems following her removal from a position on the authority's cabinet but had ceased contacted after feeling she had "exhausted herself" and all the options for help.
The incident occurred at 4.20pm on the day in question.
Cllr Donohue-Moncrief arrived late to a meeting of the group, which Cllr Phillips was chairing.
Mrs Whiteley said: "Donohue-Moncrief sat down opposite Cllr Phillips and appeared, in the victim's words, to be in a distressed state.
"She was making eye contact with Cllr Phillips in a menacing way, a way intended to make Cllr Philips feel intimidated and she did feel intimidated."
Cllr Donohue-Moncrieff then started talking about her perceived failings and issues with the mental health triage team at the Street.
After the meeting moved on the incident came to a head when Cllr Donohue-Moncrief slammed her hand on the table.
Mrs Whiteley said: "She exploded out of her chair and, clutching papers in one hand, moved around next to Cllr Phillips and then three inches from her ear started screaming 'you don't know, you don't know'.
"Cllr Phillips said she feared she was going to be struck and could feel the spittle hitting her on her ear, she said she was thinking about when the assault would come and if it would hurt if it would break her glasses.
"Cllr Donohue-Moncrief then threw the papers on the floor and was ushered out of the meeting by some other attendees. The whole incident last about 10 to 15 seconds."
A victim impact statement from Cllr Phillips was read in court.
In it, she said she had been left traumatised following the incident.
Nick Tubbs, mitigating, said Cllr Donohue-Moncrief was sorry for her actions.
He said: "This whole incident lasted a very short amount of time and while there may have been the fear of physical violence this was not a physical assault.
"My client has been taking steps to ensure that this type of behaviour doesn't happen again and apologises.
"She hopes to continue her work on the council for the constituents who voted for her.
"She was banned from attending the Town Hall by the chief executive of Scarborough Council following the incident.
"There is a meeting with Jim Dillon on Monday next week and she wants to go back to being a councillor for the people she represents."
Cllr Donohue-Moncrief, who was elected as a Conservative but now sits as an independent, admitted to one count of common assault and was fined Â£147.
She was also ordered to pay Â£85 costs and a Â£30 victim surcharge.
Cllr Phillips, who was present for the hearing alongside Scarborough Council leader Cllr Derek Bastiman, his wife Cllr Lynn Bastiman and Mayor Cllr Martin Smith, was awarded Â£50 compensation.