Perhaps the application of network analysis as its used for the control of the Covid-19 pandemics. I did a lecture on the application on that in America with a show case: Identifying forgotten links between people etc. but I would like to publish that
Academic, scientific, professional History is nowadays the set of social sciences studying the past. The epistemological changes in History are not coming from methods but systematic enlargement of sources, objects, and problems. We don't research History anymore, only relying on past public and private written documents, but we recall oral sources, iconographies, ethnographies, and several other materials. We are much more concerned about gender, minorities, marginal groups, workers, peasants, and all the social groups silenced by traditional historiography. We have been making a significant effort to fight ethnocentric, eurocentric, and all the diverse centric, essentialist and nationalist ideological perspectives of History. Nowadays, there is also a growing scientific investment towards global subjects, transcultural domains, and connective History. Since historiography was primarily dominated by national History, it is still the main framework of most Ph.D. theses, and global, connective, or transcultural studies are rare.
This is a very general question, so I'll give a very general answer.
1. Analysis of the knowledge circulation of your subject. From where did the subject come, and perhaps more important in what way was it converted when it became the subject that you study?
2. Usage of intersectional theory in broader analysis. As Ivo Carneiro de Sousa already stated, currently a lot of work is put into correcting the negative tendencies (justifying racisms, eugenics, sexism, and cultural superiority complexes) that the subject of history has brought in the past. Analyzing your reserch subject through ideas of race, gender, class, and pereferia/center. This method is also very applicable with method nr. 1.
In the more specific fields of history such as economic, intellectual, local, military history etc. there are always new and innovative research published. From looking at your publications you seem to be mostly focused on the history of education, language (Tamil-Brahmi) and media. Perhaps try to ask a dedicated historian in one of those subjects for recommendations for innovative methods specific to the field and/or works that use innovative methods?
That is clear, but the department of practical i.e. investigative history is now 221B Baker Street, London. Even for discovered but lost history - the latter was the reason for Richard Hakluyt to work for a chair of oversea history in his time and the Hakluyt Society to publish document in a compact series
Using multidisciplinary methodology/approach makes historical study scientific and innovative. This gives it a wider outreach to decipher problems and proffer solutions to everyday societal issues (political, economic, gender, education, security, cultural etc).