< b="" />Introduction< />
In this question, we are asked to identify the periodical that is not correctly matched with its editor. We are given four options: Bande Mataram, New India, Yugantar, and Sandhya, along with their respective editors: Aurobindo Ghosh, Bipin Chandra Pal, Bhupendranath Dutta, and Barindra Ghosh. We need to determine which of these combinations is incorrect.

< b="" />Explanation< />
To find the incorrect combination, we can analyze the periodicals and their editors individually.

< b="" />1. Bande Mataram : Aurobindo Ghosh< />
Bande Mataram was an influential nationalist newspaper published in Kolkata during the Indian independence movement. It was initially started by Bipin Chandra Pal, but later Aurobindo Ghosh became the editor of the newspaper. Therefore, the combination of Bande Mataram with Aurobindo Ghosh as its editor is correct.

< b="" />2. New India : Bipin Chandra Pal< />
New India was a newspaper founded by Bipin Chandra Pal in 1905. He served as its editor and played a significant role in promoting nationalism and advocating for Indian independence. Therefore, the combination of New India with Bipin Chandra Pal as its editor is also correct.

< b="" />3. Yugantar : Bhupendranath Dutta< />
Yugantar was a Bengali revolutionary newspaper published during the early 20th century. Bhupendranath Dutta, along with his brother Barindra Ghosh, played a crucial role in editing and publishing Yugantar. Therefore, the combination of Yugantar with Bhupendranath Dutta as its editor is correct.

< b="" />4. Sandhya : Barindra Ghosh< />
Sandhya was a Bengali newspaper founded by Barindra Ghosh, the younger brother of Aurobindo Ghosh. Barindra Ghosh served as the editor of Sandhya. However, according to the given options, Sandhya is incorrectly matched with Barindra Ghosh as its editor. The correct combination should be Barindra Ghosh as the editor of Yugantar, not Sandhya.

< b="" />Conclusion< />
Based on the analysis, we can conclude that the periodical that is not correctly matched with its editor is Sandhya with Barindra Ghosh as its editor.