During the time Barks drew his comic book stories the USA was swept with waves of morals codes which were intended to save the young readers from certain topics; no mentioning of death, no excessive violence, no unnecessary pain, no adult themes, no sex, no showing of crooked lawmen, and many more. Barks was always very careful not to cross the boundaries, but in a few instances his publishers felt he had, which resulted in rejected stories:
In 1945 Barks drew a 10-page Christmas story intended for WDCS064 and later known as 'Silent Night', in which Donald Duck quarrels with neighbour Jones while he and the nephews are attempting to sing carols. In the end scene Donald is tortured with an electric cattle prod. Western found the story far too violent and it was not published until 1990 when it appeared in the CBL (Carl Barks Library).
In 1952 Barks made another 10-page story intended for WDCS144 and later known as 'The Golden Apples' but it was vetoed by Western. It has since been lost. To the best of Barks' recollection it was based on the Greek myth of The Apples of the Hesperides, and took place during an apple festival at which Daisy appeared as a jealous and crusty battleaxe and that got it rejected. See more HERE.
Even as late as 1957 Barks wrote a 10-pager which was deemed unsuitable for publication. It was intended for WDCS196 and would - again to the best of Barks' recollection - have been titled 'Bobsled Race'. The plot circled around violent arguments between Donald and the nephews. It is now lost. One year before Western had warned Barks that he was to tone down the violent relationship between the two parties as a direct result of a complaint from a mother. She had objected to Donald saying 'Shut up' to his nephews in the closing panel of WDCS186 'Ice Taxies'.
The same year another 10-pager, intended for WDCS 215, was shelved. It was simply archived as 'The Milkman Story' and it tells a tale about Donald being a perfect milkman until he becomes extremely violent and revengeful towards a very irritating customer. The story was finally published in the Dutch Donald Duck magazine #47 from 1974, and - after having been published in several other European countries - in WDCS550 in 1990.

On rare occasions Barks was requested to draw stories from professional scriptwriters. It started in 1943 when he received a rough script from Western on the topic of Donald having difficulties cultivating his vegetable garden. Barks found the script so weak that he, on his own accord, took upon himself to improve it. The result is well known; WDCS0031 'Victory Garden' became Barks' first 10-pager.
The following year and until 1947 Barks was requested by his publisher to draw already scripted stories with characters other than those from his already well-established duck universe. The initial reason being that many of Western's staff artists were away on war duty, but Barks was there and able to fill the void with stories chiefly focussing on the characters Benny Burro and Barney Bear. He also made one story featuring Porky Pig and Bugs Bunny, FC0048 Porky of the Mounties, but Western found that the latter's face was so incorrectly done by Barks that he was freed from making any more stories with the character. See more HERE.
In 1945 Western ordered Barks to try his hand with a story from the mouse universe, and Barks reluctantly accepted and just drew the story as it was scripted. The result was FC0079 The Riddle of the Red Hat, a story that neither Western nor Barks had reason to be proud of. See more HERE.
In 1952 Barks - for the only time in his career - made a story based on a film script. The Disney Company was producing a Donald short with Halloween as the main theme and they needed a comic book story to be released simultaneously. Barks was chosen and the result was DD26 Trick or Treat, titled after the film. In it Barks tried to strengthen the plot by adding several scenes of his own, but they were turned down by Western. See more HERE.

In 1959 Western introduced two special series titled Grandma Duck's Farm Friends (see more HERE - comic books FC1010, FC1073, FC1161) and Daisy Duck's Diary (see more HERE - comic books FC1055, FC1150) featuring short stories (generally 6 to 8 pages) with the two ladies. Barks participated with a number of stories in the above mentioned issues mainly by drawing and inking other artists stories. He regarded the work as a nice break because it meant easy money, and he did not have to do the writing which was not that well-paid anyway. Fans will agree that the plots are sub-standard to Barks' own creations.
In 1954 Barks made a to-order story for three local electricity companies, who wanted to inform the young readers about the hazards connected with their product through so-called Giveaways, i.e. free comic books. The writer is unknown, but it was probably a merger between the companies' public relations departments and Western. A similar idea had been launched the year before in KG Pinocchio Learns About Kites with Carl Buettner as the graphic artist, and, evidently, the main idea could stand a repetition. Barks' version (he actually made one version for each company with a few differences) was KG Donald Duck Tells about Kites, a sort of instructional 'documentary' more than a coherent story. See more HERE.

The fanzine The Duckburg Times did, in fact, attempt to make a poll in their #15 issue from 1982 over Barks' own worst stories. The votes fell on the above stories (presented in chronological order!): FC0203 The Golden Christmas Tree (1948), DD60 The Titanic Ants (1958), U$53 Interplanetary Postman (1964), WDCS297 Monkey Business (1965), and U$62 Queen of the Wild Dog Pack (1966).
The poll can by no means be described as being near to a representative fan participation (only a puny 36 votes were cast), which just goes to show that Barks in his readers' minds never did make a Worst Story that the readers can agree on...