Firstly the below legislation requires authorities to advertise planning applications in specific circumstances.
The Town and Country Planning (Development Management Procedure)(Scotland) Regulations 2013 Part 4 Regulation 20
Publication of application by the planning authority
20.—(1) Subject to paragraphs (3) to [F1(6) and regulation 20A], in the circumstances specified in paragraph (2) the planning authority must publish a notice in the form set out in Schedule 4 in a newspaper circulating in the locality in which the neighbouring land is situated.
(2) The circumstances are
(a)it is not possible for the planning authority to carry out notification in terms of regulation 18 because there are no premises situated on the neighbouring land to which the notification can be sent;
(b)the applicant has submitted with an application for planning permission under regulations 9, 10 or 11 a certificate issued under regulation 15(2)(b)(iii);
(c)the application is made under regulation 9, 10 or 11 and relates to development of one or more of the classes of development specified in Schedule 3, or
(d)the application is made under regulation 9, 10 or 11 and relates to development which does not accord with the provisions of the development plan;
[F2(e)the application is made under regulation 9, 10 or 11 and relates to development falling within paragraphs 3, 3A or 4 of Schedule 5.]
(3) Paragraph (2)(a) does not apply where—
(a)all the neighbouring land referred to in that paragraph is owned by the planning authority or by the applicant; or
(b)the application relates to householder development.
Secondly the legislative basis for making a charge is listed here.
https://www.legislation.gov.uk/sdsi/2009/9780111005262
The Town and Country Planning (Charges for Publication of Notices)(Scotland) Regulations 2009
Recovery of cost of publication
2.—(1) Where a planning authority publish a notice in a newspaper in accordance with regulation 20(1) of the 2008 Regulations they are to charge the cost of publishing that notice to the applicant in accordance with paragraphs (2) and (3).
(2) The planning authority are to notify the applicant in writing of the cost of publication of the notice, calculated in accordance with paragraph (3), and the applicant must, within 21 days of being so notified, pay to the planning authority a sum equal to that cost.
(3) Where the advertisement by which notice is published relates to–
(a)one application only, the cost of publication is the amount paid by the planning authority for that advertisement;
(b)more than one application, the cost of publication in respect of each application is the amount paid by the planning authority for that advertisement divided by the number of applications to which it relates.